effect stringclasses 48
values | original_source_type stringlengths 0 23k | opens_and_abbrevs listlengths 2 92 | isa_cross_project_example bool 1
class | source_definition stringlengths 9 57.9k | partial_definition stringlengths 7 23.3k | is_div bool 2
classes | is_type null | is_proof bool 2
classes | completed_definiton stringlengths 1 250k | dependencies dict | effect_flags listlengths 0 2 | ideal_premises listlengths 0 236 | mutual_with listlengths 0 11 | file_context stringlengths 0 407k | interleaved bool 1
class | is_simply_typed bool 2
classes | file_name stringlengths 5 48 | vconfig dict | is_simple_lemma null | source_type stringlengths 10 23k | proof_features listlengths 0 1 | name stringlengths 8 95 | source dict | verbose_type stringlengths 1 7.42k | source_range dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "SAEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.HPKE",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module"... | false | let max_length_info (a:S.hash_algorithm) =
max_size_t - S.size_label_version - S.size_suite_id_hpke - S.size_label_info_hash - Spec.Hash.Definitions.block_length a | let max_length_info (a: S.hash_algorithm) = | false | null | false | max_size_t - S.size_label_version - S.size_suite_id_hpke - S.size_label_info_hash -
Spec.Hash.Definitions.block_length a | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.hash_algorithm",
"Prims.op_Subtraction",
"Lib.IntTypes.max_size_t",
"Spec.Agile.HPKE.size_label_version",
"Spec.Agile.HPKE.size_suite_id_hpke",
"Spec.Agile.HPKE.size_label_info_hash",
"Spec.Hash.Definitions.block_length",
"Prims.int"
] | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val max_length_info : a: Spec.Agile.HPKE.hash_algorithm -> Prims.int | [] | Hacl.Impl.HPKE.max_length_info | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Spec.Agile.HPKE.hash_algorithm -> Prims.int | {
"end_col": 122,
"end_line": 29,
"start_col": 2,
"start_line": 29
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "SAEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.HPKE",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module"... | false | let serialized_point_dh (cs:S.ciphersuite) = lbuffer uint8 (size (S.size_dh_serialized cs)) | let serialized_point_dh (cs: S.ciphersuite) = | false | null | false | lbuffer uint8 (size (S.size_dh_serialized cs)) | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Lib.Buffer.lbuffer",
"Lib.IntTypes.uint8",
"Lib.IntTypes.size",
"Spec.Agile.HPKE.size_dh_serialized"
] | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val serialized_point_dh : cs: Spec.Agile.HPKE.ciphersuite -> Type0 | [] | Hacl.Impl.HPKE.serialized_point_dh | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Type0 | {
"end_col": 91,
"end_line": 20,
"start_col": 45,
"start_line": 20
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "SAEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.HPKE",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module"... | false | let key_aead (cs:S.ciphersuite) = lbuffer uint8 (size (S.size_aead_key cs)) | let key_aead (cs: S.ciphersuite) = | false | null | false | lbuffer uint8 (size (S.size_aead_key cs)) | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Lib.Buffer.lbuffer",
"Lib.IntTypes.uint8",
"Lib.IntTypes.size",
"Spec.Agile.HPKE.size_aead_key"
] | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val key_aead : cs: Spec.Agile.HPKE.ciphersuite -> Type0 | [] | Hacl.Impl.HPKE.key_aead | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Type0 | {
"end_col": 75,
"end_line": 22,
"start_col": 34,
"start_line": 22
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "SAEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.HPKE",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module"... | false | let key_dh_secret (cs:S.ciphersuite) = lbuffer uint8 (size (S.size_dh_key cs)) | let key_dh_secret (cs: S.ciphersuite) = | false | null | false | lbuffer uint8 (size (S.size_dh_key cs)) | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Lib.Buffer.lbuffer",
"Lib.IntTypes.uint8",
"Lib.IntTypes.size",
"Spec.Agile.HPKE.size_dh_key"
] | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val key_dh_secret : cs: Spec.Agile.HPKE.ciphersuite -> Type0 | [] | Hacl.Impl.HPKE.key_dh_secret | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Type0 | {
"end_col": 78,
"end_line": 18,
"start_col": 39,
"start_line": 18
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "SAEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.HPKE",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module"... | false | let nonce_aead (cs:S.ciphersuite) = lbuffer uint8 (size (S.size_aead_nonce cs)) | let nonce_aead (cs: S.ciphersuite) = | false | null | false | lbuffer uint8 (size (S.size_aead_nonce cs)) | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Lib.Buffer.lbuffer",
"Lib.IntTypes.uint8",
"Lib.IntTypes.size",
"Spec.Agile.HPKE.size_aead_nonce"
] | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val nonce_aead : cs: Spec.Agile.HPKE.ciphersuite -> Type0 | [] | Hacl.Impl.HPKE.nonce_aead | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Type0 | {
"end_col": 79,
"end_line": 24,
"start_col": 36,
"start_line": 24
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.HKDF",
"short_module": "HKDF"
},
{
"... | false | let setupBaseR_st (cs:S.ciphersuite) (p:Type0) =
o_ctx : context_s cs
-> pkE: key_dh_public cs
-> skR: key_dh_secret cs
-> infolen: size_t{v infolen <= max_length_info (S.hash_of_cs cs)}
-> info: lbuffer uint8 infolen
-> Stack UInt32.t
(requires fun h0 ->
p /\
ctx_invariant h0 o_ctx ... | let setupBaseR_st (cs: S.ciphersuite) (p: Type0) = | false | null | false |
o_ctx: context_s cs ->
pkE: key_dh_public cs ->
skR: key_dh_secret cs ->
infolen: size_t{v infolen <= max_length_info (S.hash_of_cs cs)} ->
info: lbuffer uint8 infolen
-> Stack UInt32.t
(requires
fun h0 ->
p /\ ctx_invariant h0 o_ctx /\ live h0 pkE /\ live h0 skR /\ live h... | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Hacl.Impl.HPKE.context_s",
"Hacl.Impl.HPKE.key_dh_public",
"Hacl.Impl.HPKE.key_dh_secret",
"Lib.IntTypes.size_t",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Lib.IntTypes.v",
"Lib.IntTypes.U32",
"Lib.IntTypes.PUB",
"Hacl.Impl.HPKE.max_length_info",
"Spec.Agile.HPK... | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val setupBaseR_st : cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | [] | Hacl.Impl.HPKE.setupBaseR_st | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | {
"end_col": 6,
"end_line": 91,
"start_col": 5,
"start_line": 71
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.HKDF",
"short_module": "HKDF"
},
{
"... | false | let setupBaseS_st (cs:S.ciphersuite) (p:Type0) =
o_pkE: key_dh_public cs
-> o_ctx: context_s cs
-> skE: key_dh_secret cs
-> pkR: serialized_point_dh cs
-> infolen: size_t{v infolen <= max_length_info (S.hash_of_cs cs)}
-> info: lbuffer uint8 infolen
-> Stack UInt32.t
(requires fun h0 ->
p ... | let setupBaseS_st (cs: S.ciphersuite) (p: Type0) = | false | null | false |
o_pkE: key_dh_public cs ->
o_ctx: context_s cs ->
skE: key_dh_secret cs ->
pkR: serialized_point_dh cs ->
infolen: size_t{v infolen <= max_length_info (S.hash_of_cs cs)} ->
info: lbuffer uint8 infolen
-> Stack UInt32.t
(requires
fun h0 ->
p /\ live h0 o_pkE /\ ctx_inva... | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Hacl.Impl.HPKE.key_dh_public",
"Hacl.Impl.HPKE.context_s",
"Hacl.Impl.HPKE.key_dh_secret",
"Hacl.Impl.HPKE.serialized_point_dh",
"Lib.IntTypes.size_t",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Lib.IntTypes.v",
"Lib.IntTypes.U32",
"Lib.IntTypes.PUB",
"Hacl.Impl.... | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val setupBaseS_st : cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | [] | Hacl.Impl.HPKE.setupBaseS_st | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | {
"end_col": 6,
"end_line": 67,
"start_col": 5,
"start_line": 43
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.HKDF",
"short_module": "HKDF"
},
{
"... | false | let openBase_st (cs:S.ciphersuite) (p:Type0) =
pkE: key_dh_public cs { S.is_valid_not_export_only_ciphersuite cs }
-> skR: key_dh_secret cs
-> infolen: size_t {v infolen <= max_length_info (S.hash_of_cs cs)}
-> info: lbuffer uint8 infolen
-> aadlen: size_t {v aadlen <= SAEAD.max_length (S.aead_alg_of cs)}
... | let openBase_st (cs: S.ciphersuite) (p: Type0) = | false | null | false |
pkE: key_dh_public cs {S.is_valid_not_export_only_ciphersuite cs} ->
skR: key_dh_secret cs ->
infolen: size_t{v infolen <= max_length_info (S.hash_of_cs cs)} ->
info: lbuffer uint8 infolen ->
aadlen: size_t{v aadlen <= SAEAD.max_length (S.aead_alg_of cs)} ->
aad: lbuffer uint8 aadlen ->
ctl... | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Hacl.Impl.HPKE.key_dh_public",
"Prims.b2t",
"Spec.Agile.HPKE.is_valid_not_export_only_ciphersuite",
"Hacl.Impl.HPKE.key_dh_secret",
"Lib.IntTypes.size_t",
"Prims.op_LessThanOrEqual",
"Lib.IntTypes.v",
"Lib.IntTypes.U32",
"Lib.IntTypes.PUB",
"Hacl.Impl.HPKE.max_len... | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val openBase_st : cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | [] | Hacl.Impl.HPKE.openBase_st | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | {
"end_col": 8,
"end_line": 160,
"start_col": 5,
"start_line": 134
} | |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Hacl.HPKE.Interface.HKDF",
"short_module": "HKDF"
},
{
"... | false | let sealBase_st (cs:S.ciphersuite) (p:Type0) =
skE: key_dh_secret cs { S.is_valid_not_export_only_ciphersuite cs }
-> pkR: serialized_point_dh cs
-> infolen: size_t {v infolen <= max_length_info (S.hash_of_cs cs)}
-> info: lbuffer uint8 infolen
-> aadlen: size_t {v aadlen <= SAEAD.max_length (S.aead_alg_of... | let sealBase_st (cs: S.ciphersuite) (p: Type0) = | false | null | false |
skE: key_dh_secret cs {S.is_valid_not_export_only_ciphersuite cs} ->
pkR: serialized_point_dh cs ->
infolen: size_t{v infolen <= max_length_info (S.hash_of_cs cs)} ->
info: lbuffer uint8 infolen ->
aadlen: size_t{v aadlen <= SAEAD.max_length (S.aead_alg_of cs)} ->
aad: lbuffer uint8 aadlen ->
... | {
"checked_file": "Hacl.Impl.HPKE.fsti.checked",
"dependencies": [
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"FStar.UI... | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Hacl.Impl.HPKE.key_dh_secret",
"Prims.b2t",
"Spec.Agile.HPKE.is_valid_not_export_only_ciphersuite",
"Hacl.Impl.HPKE.serialized_point_dh",
"Lib.IntTypes.size_t",
"Prims.op_LessThanOrEqual",
"Lib.IntTypes.v",
"Lib.IntTypes.U32",
"Lib.IntTypes.PUB",
"Hacl.Impl.HPKE.m... | [] | module Hacl.Impl.HPKE
open FStar.HyperStack
open FStar.HyperStack.All
module B = LowStar.Buffer
open Lib.Buffer
open Lib.IntTypes
module S = Spec.Agile.HPKE
module SAEAD = Spec.Agile.AEAD
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
inline_for_extraction noextract
let key_dh_public (cs:S.ciphersuite) = ... | false | true | Hacl.Impl.HPKE.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val sealBase_st : cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | [] | Hacl.Impl.HPKE.sealBase_st | {
"file_name": "code/hpke/Hacl.Impl.HPKE.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> p: Type0 -> Type0 | {
"end_col": 8,
"end_line": 129,
"start_col": 5,
"start_line": 100
} | |
Prims.Tot | val hash_sha256:Hash.hash_st Spec.Agile.Hash.SHA2_256 | [
{
"abbrev": true,
"full_module": "Hacl.Hash.Definitions",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.HPKE",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Hacl.HPKE.Interface",
"short_module": null
},
{
"abbrev": false,
"... | false | let hash_sha256 : Hash.hash_st Spec.Agile.Hash.SHA2_256 =
Hacl.Streaming.SHA2.hash_256 | val hash_sha256:Hash.hash_st Spec.Agile.Hash.SHA2_256
let hash_sha256:Hash.hash_st Spec.Agile.Hash.SHA2_256 = | false | null | false | Hacl.Streaming.SHA2.hash_256 | {
"checked_file": "Hacl.HPKE.Interface.Hash.fst.checked",
"dependencies": [
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"prims.fst.checked",
"Meta.Attribute.fst.checked",
"Hacl.Streaming.SHA2.fst.checked",
"Hacl.Hash.Definitions.fst.checked",
"FStar.Pervasives.fsti.ch... | [
"total"
] | [
"Hacl.Streaming.SHA2.hash_256"
] | [] | module Hacl.HPKE.Interface.Hash
module S = Spec.Agile.HPKE
module Hash = Hacl.Hash.Definitions
[@ Meta.Attribute.specialize ]
noextract
assume val hash: #cs:S.ciphersuite -> Hash.hash_st (S.hash_of_cs cs)
(** Instantiations of hash **)
inline_for_extraction noextract | false | true | Hacl.HPKE.Interface.Hash.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val hash_sha256:Hash.hash_st Spec.Agile.Hash.SHA2_256 | [] | Hacl.HPKE.Interface.Hash.hash_sha256 | {
"file_name": "code/hpke/Hacl.HPKE.Interface.Hash.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Hash.Definitions.hash_st Spec.Hash.Definitions.SHA2_256 | {
"end_col": 30,
"end_line": 14,
"start_col": 2,
"start_line": 14
} |
Prims.Tot | val hash_sha512:Hash.hash_st Spec.Agile.Hash.SHA2_512 | [
{
"abbrev": true,
"full_module": "Hacl.Hash.Definitions",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.HPKE",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Hacl.HPKE.Interface",
"short_module": null
},
{
"abbrev": false,
"... | false | let hash_sha512 : Hash.hash_st Spec.Agile.Hash.SHA2_512 =
Hacl.Streaming.SHA2.hash_512 | val hash_sha512:Hash.hash_st Spec.Agile.Hash.SHA2_512
let hash_sha512:Hash.hash_st Spec.Agile.Hash.SHA2_512 = | false | null | false | Hacl.Streaming.SHA2.hash_512 | {
"checked_file": "Hacl.HPKE.Interface.Hash.fst.checked",
"dependencies": [
"Spec.Agile.HPKE.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"prims.fst.checked",
"Meta.Attribute.fst.checked",
"Hacl.Streaming.SHA2.fst.checked",
"Hacl.Hash.Definitions.fst.checked",
"FStar.Pervasives.fsti.ch... | [
"total"
] | [
"Hacl.Streaming.SHA2.hash_512"
] | [] | module Hacl.HPKE.Interface.Hash
module S = Spec.Agile.HPKE
module Hash = Hacl.Hash.Definitions
[@ Meta.Attribute.specialize ]
noextract
assume val hash: #cs:S.ciphersuite -> Hash.hash_st (S.hash_of_cs cs)
(** Instantiations of hash **)
inline_for_extraction noextract
let hash_sha256 : Hash.hash_st Spec.Agile.Hash.S... | false | true | Hacl.HPKE.Interface.Hash.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val hash_sha512:Hash.hash_st Spec.Agile.Hash.SHA2_512 | [] | Hacl.HPKE.Interface.Hash.hash_sha512 | {
"file_name": "code/hpke/Hacl.HPKE.Interface.Hash.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Hash.Definitions.hash_st Spec.Hash.Definitions.SHA2_512 | {
"end_col": 30,
"end_line": 17,
"start_col": 2,
"start_line": 17
} |
FStar.Pervasives.Lemma | val mem_index (#a:eqtype) (x:a) (s:seq a)
: Lemma (requires (mem x s))
(ensures (exists i. index s i == x)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let mem_index = mem_index' | val mem_index (#a:eqtype) (x:a) (s:seq a)
: Lemma (requires (mem x s))
(ensures (exists i. index s i == x))
let mem_index = | false | null | true | mem_index' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.mem_index'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val mem_index (#a:eqtype) (x:a) (s:seq a)
: Lemma (requires (mem x s))
(ensures (exists i. index s i == x)) | [] | FStar.Seq.Properties.mem_index | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: a -> s: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma (requires FStar.Seq.Properties.mem x s)
(ensures exists (i: Prims.nat{i < FStar.Seq.Base.length s}). FStar.Seq.Base.index s i == x) | {
"end_col": 26,
"end_line": 60,
"start_col": 16,
"start_line": 60
} |
FStar.Pervasives.Lemma | val lemma_mem_count: #a:eqtype -> s:seq a -> f:(a -> Tot bool) -> Lemma
(requires (forall (i:nat{i<length s}). f (index s i)))
(ensures (forall (x:a). mem x s ==> f x)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_mem_count = lemma_mem_count' | val lemma_mem_count: #a:eqtype -> s:seq a -> f:(a -> Tot bool) -> Lemma
(requires (forall (i:nat{i<length s}). f (index s i)))
(ensures (forall (x:a). mem x s ==> f x))
let lemma_mem_count = | false | null | true | lemma_mem_count' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.lemma_mem_count'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_mem_count: #a:eqtype -> s:seq a -> f:(a -> Tot bool) -> Lemma
(requires (forall (i:nat{i<length s}). f (index s i)))
(ensures (forall (x:a). mem x s ==> f x)) | [] | FStar.Seq.Properties.lemma_mem_count | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma
(requires forall (i: Prims.nat{i < FStar.Seq.Base.length s}). f (FStar.Seq.Base.index s i))
(ensures forall (x: a). FStar.Seq.Properties.mem x s ==> f x) | {
"end_col": 38,
"end_line": 125,
"start_col": 22,
"start_line": 125
} |
FStar.Pervasives.Lemma | val sorted_concat_lemma: #a:eqtype
-> f:(a -> a -> Tot bool){total_order a f}
-> lo:seq a{sorted f lo}
-> pivot:a
-> hi:seq a{sorted f hi}
-> Lemma (requires (forall y. (mem y lo ==> f y pivot)
... | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let sorted_concat_lemma = sorted_concat_lemma' | val sorted_concat_lemma: #a:eqtype
-> f:(a -> a -> Tot bool){total_order a f}
-> lo:seq a{sorted f lo}
-> pivot:a
-> hi:seq a{sorted f hi}
-> Lemma (requires (forall y. (mem y lo ==> f y pivot)
... | false | null | true | sorted_concat_lemma' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.sorted_concat_lemma'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val sorted_concat_lemma: #a:eqtype
-> f:(a -> a -> Tot bool){total_order a f}
-> lo:seq a{sorted f lo}
-> pivot:a
-> hi:seq a{sorted f hi}
-> Lemma (requires (forall y. (mem y lo ==> f y pivot)
... | [] | FStar.Seq.Properties.sorted_concat_lemma | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
f: (_: a -> _: a -> Prims.bool){FStar.Seq.Properties.total_order a f} ->
lo: FStar.Seq.Base.seq a {FStar.Seq.Properties.sorted f lo} ->
pivot: a ->
hi: FStar.Seq.Base.seq a {FStar.Seq.Properties.sorted f hi}
-> FStar.Pervasives.Lemma
(requires
forall (y: a).
(FStar.Seq.Propert... | {
"end_col": 46,
"end_line": 148,
"start_col": 26,
"start_line": 148
} |
FStar.Pervasives.Lemma | val lemma_list_seq_bij: #a:Type -> l:list a -> Lemma
(requires (True))
(ensures (seq_to_list (seq_of_list l) == l)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let lemma_list_seq_bij = lemma_list_seq_bij' | val lemma_list_seq_bij: #a:Type -> l:list a -> Lemma
(requires (True))
(ensures (seq_to_list (seq_of_list l) == l))
let lemma_list_seq_bij = | false | null | true | lemma_list_seq_bij' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.lemma_list_seq_bij'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_list_seq_bij: #a:Type -> l:list a -> Lemma
(requires (True))
(ensures (seq_to_list (seq_of_list l) == l)) | [] | FStar.Seq.Properties.lemma_list_seq_bij | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a
-> FStar.Pervasives.Lemma
(ensures FStar.Seq.Properties.seq_to_list (FStar.Seq.Properties.seq_of_list l) == l) | {
"end_col": 44,
"end_line": 423,
"start_col": 25,
"start_line": 423
} |
FStar.Pervasives.Lemma | val lemma_split : #a:Type -> s:seq a -> i:nat{(0 <= i /\ i <= length s)} -> Lemma
(ensures (append (fst (split s i)) (snd (split s i)) == s)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_split #_ s i =
cut (equal (append (fst (split s i)) (snd (split s i))) s) | val lemma_split : #a:Type -> s:seq a -> i:nat{(0 <= i /\ i <= length s)} -> Lemma
(ensures (append (fst (split s i)) (snd (split s i)) == s))
let lemma_split #_ s i = | false | null | true | cut (equal (append (fst (split s i)) (snd (split s i))) s) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append",
"FStar.Pervasives.Native.fst",
"FStar.Seq.Properties.split",
"FStar.Pervasives.Native.snd",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_split : #a:Type -> s:seq a -> i:nat{(0 <= i /\ i <= length s)} -> Lemma
(ensures (append (fst (split s i)) (snd (split s i)) == s)) | [] | FStar.Seq.Properties.lemma_split | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat{0 <= i /\ i <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Base.append (FStar.Pervasives.Native.fst (FStar.Seq.Properties.split s i))
(FStar.Pervasives.Native.snd (FStar.Seq.Properties.split s i)) ==
s) | {
"end_col": 61,
"end_line": 50,
"start_col": 2,
"start_line": 50
} |
FStar.Pervasives.Lemma | val lemma_cons_inj: #a:Type -> v1:a -> v2:a -> s1:seq a -> s2:seq a
-> Lemma (requires (equal (cons v1 s1) (cons v2 s2)))
(ensures (v1 == v2 /\ equal s1 s2)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_cons_inj #_ v1 v2 s1 s2 =
let t1 = create 1 v1 in
let t2 = create 1 v2 in
lemma_append_inj t1 s1 t2 s2;
assert(index t1 0 == index t2 0) | val lemma_cons_inj: #a:Type -> v1:a -> v2:a -> s1:seq a -> s2:seq a
-> Lemma (requires (equal (cons v1 s1) (cons v2 s2)))
(ensures (v1 == v2 /\ equal s1 s2))
let lemma_cons_inj #_ v1 v2 s1 s2 = | false | null | true | let t1 = create 1 v1 in
let t2 = create 1 v2 in
lemma_append_inj t1 s1 t2 s2;
assert (index t1 0 == index t2 0) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims._assert",
"Prims.eq2",
"FStar.Seq.Base.index",
"Prims.unit",
"FStar.Seq.Properties.lemma_append_inj",
"FStar.Seq.Base.create"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_cons_inj: #a:Type -> v1:a -> v2:a -> s1:seq a -> s2:seq a
-> Lemma (requires (equal (cons v1 s1) (cons v2 s2)))
(ensures (v1 == v2 /\ equal s1 s2)) | [] | FStar.Seq.Properties.lemma_cons_inj | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | v1: a -> v2: a -> s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(requires
FStar.Seq.Base.equal (FStar.Seq.Properties.cons v1 s1) (FStar.Seq.Properties.cons v2 s2))
(ensures v1 == v2 /\ FStar.Seq.Base.equal s1 s2) | {
"end_col": 34,
"end_line": 47,
"start_col": 35,
"start_line": 43
} |
FStar.Pervasives.Lemma | val upd_slice: #a:Type -> s:seq a -> i:nat -> j:nat{i <= j /\ j <= length s}
-> k:nat{k < j - i} -> v:a -> Lemma
(requires i + k < j)
(ensures upd (slice s i j) k v == slice (upd s (i + k) v) i j)
[SMTPat (upd (slice s i j) k v)] | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let upd_slice #_ s i j k v =
lemma_eq_intro (upd (slice s i j) k v) (slice (upd s (i + k) v) i j) | val upd_slice: #a:Type -> s:seq a -> i:nat -> j:nat{i <= j /\ j <= length s}
-> k:nat{k < j - i} -> v:a -> Lemma
(requires i + k < j)
(ensures upd (slice s i j) k v == slice (upd s (i + k) v) i j)
[SMTPat (upd (slice s i j) k v)]
let upd_slice #_ s i j k v = | false | null | true | lemma_eq_intro (upd (slice s i j) k v) (slice (upd s (i + k) v) i j) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"Prims.op_LessThan",
"Prims.op_Subtraction",
"FStar.Seq.Base.lemma_eq_intro",
"FStar.Seq.Base.upd",
"FStar.Seq.Base.slice",
"Prims.op_Addition",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val upd_slice: #a:Type -> s:seq a -> i:nat -> j:nat{i <= j /\ j <= length s}
-> k:nat{k < j - i} -> v:a -> Lemma
(requires i + k < j)
(ensures upd (slice s i j) k v == slice (upd s (i + k) v) i j)
[SMTPat (upd (slice s i j) k v)] | [] | FStar.Seq.Properties.upd_slice | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
i: Prims.nat ->
j: Prims.nat{i <= j /\ j <= FStar.Seq.Base.length s} ->
k: Prims.nat{k < j - i} ->
v: a
-> FStar.Pervasives.Lemma (requires i + k < j)
(ensures
FStar.Seq.Base.upd (FStar.Seq.Base.slice s i j) k v ==
FStar.Seq.Base.slice (FStar.Seq.B... | {
"end_col": 70,
"end_line": 78,
"start_col": 2,
"start_line": 78
} |
FStar.Pervasives.Lemma | val slice_upd: #a:Type -> s:seq a -> i:nat -> j:nat{i <= j /\ j <= length s}
-> k:nat{k < length s} -> v:a -> Lemma
(requires k < i \/ j <= k)
(ensures slice (upd s k v) i j == slice s i j)
[SMTPat (slice (upd s k v) i j)] | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let slice_upd #_ s i j k v =
lemma_eq_intro (slice (upd s k v) i j) (slice s i j) | val slice_upd: #a:Type -> s:seq a -> i:nat -> j:nat{i <= j /\ j <= length s}
-> k:nat{k < length s} -> v:a -> Lemma
(requires k < i \/ j <= k)
(ensures slice (upd s k v) i j == slice s i j)
[SMTPat (slice (upd s k v) i j)]
let slice_upd #_ s i j k v = | false | null | true | lemma_eq_intro (slice (upd s k v) i j) (slice s i j) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"Prims.op_LessThan",
"FStar.Seq.Base.lemma_eq_intro",
"FStar.Seq.Base.slice",
"FStar.Seq.Base.upd",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val slice_upd: #a:Type -> s:seq a -> i:nat -> j:nat{i <= j /\ j <= length s}
-> k:nat{k < length s} -> v:a -> Lemma
(requires k < i \/ j <= k)
(ensures slice (upd s k v) i j == slice s i j)
[SMTPat (slice (upd s k v) i j)] | [] | FStar.Seq.Properties.slice_upd | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
i: Prims.nat ->
j: Prims.nat{i <= j /\ j <= FStar.Seq.Base.length s} ->
k: Prims.nat{k < FStar.Seq.Base.length s} ->
v: a
-> FStar.Pervasives.Lemma (requires k < i \/ j <= k)
(ensures FStar.Seq.Base.slice (FStar.Seq.Base.upd s k v) i j == FStar.Seq.Base.slice s i ... | {
"end_col": 54,
"end_line": 75,
"start_col": 2,
"start_line": 75
} |
FStar.Pervasives.Lemma | val lemma_mem_snoc : #a:eqtype -> s:Seq.seq a -> x:a ->
Lemma (ensures (forall y. mem y (snoc s x) <==> mem y s \/ x=y)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_mem_snoc #_ s x = lemma_append_count s (Seq.create 1 x) | val lemma_mem_snoc : #a:eqtype -> s:Seq.seq a -> x:a ->
Lemma (ensures (forall y. mem y (snoc s x) <==> mem y s \/ x=y))
let lemma_mem_snoc #_ s x = | false | null | true | lemma_append_count s (Seq.create 1 x) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"FStar.Seq.Properties.lemma_append_count",
"FStar.Seq.Base.create",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_mem_snoc : #a:eqtype -> s:Seq.seq a -> x:a ->
Lemma (ensures (forall y. mem y (snoc s x) <==> mem y s \/ x=y)) | [] | FStar.Seq.Properties.lemma_mem_snoc | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> x: a
-> FStar.Pervasives.Lemma
(ensures
forall (y: a).
FStar.Seq.Properties.mem y (FStar.Seq.Properties.snoc s x) <==>
FStar.Seq.Properties.mem y s \/ x = y) | {
"end_col": 65,
"end_line": 321,
"start_col": 28,
"start_line": 321
} |
FStar.Pervasives.Lemma | val find_append_some: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (Some? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s1)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let find_append_some = find_append_some' | val find_append_some: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (Some? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s1))
let find_append_some = | false | null | true | find_append_some' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.find_append_some'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_append_some: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (Some? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s1)) | [] | FStar.Seq.Properties.find_append_some | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma (requires Some? (FStar.Seq.Properties.find_l f s1))
(ensures
FStar.Seq.Properties.find_l f (FStar.Seq.Base.append s1 s2) ==
FStar.Seq.Properties.find_l f s1) | {
"end_col": 40,
"end_line": 333,
"start_col": 23,
"start_line": 333
} |
FStar.Pervasives.Lemma | val swap_frame_lo : #a:Type -> s:seq a -> lo:nat -> i:nat{lo <= i} -> j:nat{i <= j && j < length s}
-> Lemma (ensures (slice s lo i == slice (swap s i j) lo i)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let swap_frame_lo #_ s lo i j = cut (equal (slice s lo i) (slice (swap s i j) lo i)) | val swap_frame_lo : #a:Type -> s:seq a -> lo:nat -> i:nat{lo <= i} -> j:nat{i <= j && j < length s}
-> Lemma (ensures (slice s lo i == slice (swap s i j) lo i))
let swap_frame_lo #_ s lo i j = | false | null | true | cut (equal (slice s lo i) (slice (swap s i j) lo i)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.slice",
"FStar.Seq.Properties.swap",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val swap_frame_lo : #a:Type -> s:seq a -> lo:nat -> i:nat{lo <= i} -> j:nat{i <= j && j < length s}
-> Lemma (ensures (slice s lo i == slice (swap s i j) lo i)) | [] | FStar.Seq.Properties.swap_frame_lo | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
lo: Prims.nat ->
i: Prims.nat{lo <= i} ->
j: Prims.nat{i <= j && j < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Base.slice s lo i == FStar.Seq.Base.slice (FStar.Seq.Properties.swap s i j) lo i) | {
"end_col": 84,
"end_line": 260,
"start_col": 32,
"start_line": 260
} |
FStar.Pervasives.Lemma | val lemma_mem_append : #a:eqtype -> s1:seq a -> s2:seq a
-> Lemma (ensures (forall x. mem x (append s1 s2) <==> (mem x s1 || mem x s2))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_mem_append #_ s1 s2 = lemma_append_count s1 s2 | val lemma_mem_append : #a:eqtype -> s1:seq a -> s2:seq a
-> Lemma (ensures (forall x. mem x (append s1 s2) <==> (mem x s1 || mem x s2)))
let lemma_mem_append #_ s1 s2 = | false | null | true | lemma_append_count s1 s2 | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"FStar.Seq.Properties.lemma_append_count",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_mem_append : #a:eqtype -> s1:seq a -> s2:seq a
-> Lemma (ensures (forall x. mem x (append s1 s2) <==> (mem x s1 || mem x s2))) | [] | FStar.Seq.Properties.lemma_mem_append | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.mem x (FStar.Seq.Base.append s1 s2) <==>
FStar.Seq.Properties.mem x s1 || FStar.Seq.Properties.mem x s2) | {
"end_col": 56,
"end_line": 242,
"start_col": 32,
"start_line": 242
} |
FStar.Pervasives.Lemma | val lemma_slice_snoc: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s (j - 1) || mem x (slice s i (j - 1))))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_slice_snoc #_ s i j =
cut (equal (slice s i j) (append (slice s i (j - 1)) (create 1 (index s (j - 1)))));
lemma_mem_append (slice s i (j - 1)) (create 1 (index s (j - 1))) | val lemma_slice_snoc: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s (j - 1) || mem x (slice s i (j - 1)))))
let lemma_slice_snoc #_ s i j = | false | null | true | cut (equal (slice s i j) (append (slice s i (j - 1)) (create 1 (index s (j - 1)))));
lemma_mem_append (slice s i (j - 1)) (create 1 (index s (j - 1))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_mem_append",
"FStar.Seq.Base.slice",
"Prims.op_Subtraction",
"FStar.Seq.Base.create",
"FStar.Seq.Base.index... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_slice_snoc: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s (j - 1) || mem x (slice s i (j - 1))))) | [] | FStar.Seq.Properties.lemma_slice_snoc | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat -> j: Prims.nat{i < j && j <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.mem x (FStar.Seq.Base.slice s i j) <==>
x = FStar.Seq.Base.index s (j - 1) ||
FStar.Seq.Properties.mem x (FStar.Seq.Ba... | {
"end_col": 67,
"end_line": 250,
"start_col": 2,
"start_line": 249
} |
FStar.Pervasives.Lemma | val find_append_none: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s2)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let find_append_none = find_append_none' | val find_append_none: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s2))
let find_append_none = | false | null | true | find_append_none' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.find_append_none'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_append_none: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s2)) | [] | FStar.Seq.Properties.find_append_none | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma (requires None? (FStar.Seq.Properties.find_l f s1))
(ensures
FStar.Seq.Properties.find_l f (FStar.Seq.Base.append s1 s2) ==
FStar.Seq.Properties.find_l f s2) | {
"end_col": 40,
"end_line": 345,
"start_col": 23,
"start_line": 345
} |
FStar.Pervasives.Lemma | val lemma_index_is_nth: #a:Type -> s:seq a -> i:nat{i < length s} -> Lemma
(requires True)
(ensures (L.index (seq_to_list s) i == index s i)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let lemma_index_is_nth = lemma_index_is_nth' | val lemma_index_is_nth: #a:Type -> s:seq a -> i:nat{i < length s} -> Lemma
(requires True)
(ensures (L.index (seq_to_list s) i == index s i))
let lemma_index_is_nth = | false | null | true | lemma_index_is_nth' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.lemma_index_is_nth'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_index_is_nth: #a:Type -> s:seq a -> i:nat{i < length s} -> Lemma
(requires True)
(ensures (L.index (seq_to_list s) i == index s i)) | [] | FStar.Seq.Properties.lemma_index_is_nth | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat{i < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.List.Tot.Base.index (FStar.Seq.Properties.seq_to_list s) i == FStar.Seq.Base.index s i) | {
"end_col": 44,
"end_line": 435,
"start_col": 25,
"start_line": 435
} |
FStar.Pervasives.Lemma | val seq_mem_k' (#a: eqtype) (s: seq a) (n: nat{n < Seq.length s})
: Lemma (requires True) (ensures (mem (Seq.index s n) s)) (decreases n) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec seq_mem_k': #a:eqtype -> s:seq a -> n:nat{n < Seq.length s} ->
Lemma (requires True)
(ensures (mem (Seq.index s n) s))
(decreases n)
= fun #_ s n ->
if n = 0 then ()
else let tl = tail s in
seq_mem_k' tl (n - 1) | val seq_mem_k' (#a: eqtype) (s: seq a) (n: nat{n < Seq.length s})
: Lemma (requires True) (ensures (mem (Seq.index s n) s)) (decreases n)
let rec seq_mem_k': #a: eqtype -> s: seq a -> n: nat{n < Seq.length s}
-> Lemma (requires True) (ensures (mem (Seq.index s n) s)) (decreases n) = | false | null | true | fun #_ s n ->
if n = 0
then ()
else
let tl = tail s in
seq_mem_k' tl (n - 1) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.op_Equality",
"Prims.int",
"Prims.bool",
"FStar.Seq.Properties.seq_mem_k'",
"Prims.op_Subtraction",
"FStar.Seq.Properties.tail",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val seq_mem_k' (#a: eqtype) (s: seq a) (n: nat{n < Seq.length s})
: Lemma (requires True) (ensures (mem (Seq.index s n) s)) (decreases n) | [
"recursion"
] | FStar.Seq.Properties.seq_mem_k' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> n: Prims.nat{n < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma (ensures FStar.Seq.Properties.mem (FStar.Seq.Base.index s n) s)
(decreases n) | {
"end_col": 28,
"end_line": 381,
"start_col": 2,
"start_line": 378
} |
FStar.Pervasives.Lemma | val lemma_find_l_contains (#a:Type) (f:a -> Tot bool) (l:seq a)
: Lemma (requires True) (ensures Some? (find_l f l) ==> l `contains` (Some?.v (find_l f l))) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let lemma_find_l_contains = lemma_find_l_contains' | val lemma_find_l_contains (#a:Type) (f:a -> Tot bool) (l:seq a)
: Lemma (requires True) (ensures Some? (find_l f l) ==> l `contains` (Some?.v (find_l f l)))
let lemma_find_l_contains = | false | null | true | lemma_find_l_contains' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.lemma_find_l_contains'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_find_l_contains (#a:Type) (f:a -> Tot bool) (l:seq a)
: Lemma (requires True) (ensures Some? (find_l f l) ==> l `contains` (Some?.v (find_l f l))) | [] | FStar.Seq.Properties.lemma_find_l_contains | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | f: (_: a -> Prims.bool) -> l: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
Some? (FStar.Seq.Properties.find_l f l) ==>
FStar.Seq.Properties.contains l (Some?.v (FStar.Seq.Properties.find_l f l))) | {
"end_col": 50,
"end_line": 472,
"start_col": 28,
"start_line": 472
} |
FStar.Pervasives.Lemma | val lemma_swap_slice_commute : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma (ensures (slice (swap s i j) start len == (swap (slice s start len) (i - start) (j - start)))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_swap_slice_commute #_ s start i j len =
cut (equal (slice (swap s i j) start len) (swap (slice s start len) (i - start) (j - start))) | val lemma_swap_slice_commute : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma (ensures (slice (swap s i j) start len == (swap (slice s start len) (i - start) (j - start))))
let lemma_swap_slice_commute #_ s start i j len = | false | null | true | cut (equal (slice (swap s i j) start len) (swap (slice s start len) (i - start) (j - start))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.slice",
"FStar.Seq.Properties.swap",
"Prims.op_Subtraction",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_swap_slice_commute : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma (ensures (slice (swap s i j) start len == (swap (slice s start len) (i - start) (j - start)))) | [] | FStar.Seq.Properties.lemma_swap_slice_commute | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
start: Prims.nat ->
i: Prims.nat{start <= i} ->
j: Prims.nat{i <= j} ->
len: Prims.nat{j < len && len <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Base.slice (FStar.Seq.Properties.swap s i j) start len ==
FStar.Seq.Properties.... | {
"end_col": 95,
"end_line": 267,
"start_col": 2,
"start_line": 267
} |
FStar.Pervasives.Lemma | val contains_snoc : #a:Type -> s:Seq.seq a -> x:a ->
Lemma (ensures (forall y. (snoc s x) `contains` y <==> s `contains` y \/ x==y)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let contains_snoc #_ s x =
FStar.Classical.forall_intro (append_contains_equiv s (Seq.create 1 x)) | val contains_snoc : #a:Type -> s:Seq.seq a -> x:a ->
Lemma (ensures (forall y. (snoc s x) `contains` y <==> s `contains` y \/ x==y))
let contains_snoc #_ s x = | false | null | true | FStar.Classical.forall_intro (append_contains_equiv s (Seq.create 1 x)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"FStar.Classical.forall_intro",
"Prims.l_iff",
"FStar.Seq.Properties.contains",
"FStar.Seq.Base.append",
"FStar.Seq.Base.create",
"Prims.l_or",
"FStar.Seq.Properties.append_contains_equiv",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val contains_snoc : #a:Type -> s:Seq.seq a -> x:a ->
Lemma (ensures (forall y. (snoc s x) `contains` y <==> s `contains` y \/ x==y)) | [] | FStar.Seq.Properties.contains_snoc | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> x: a
-> FStar.Pervasives.Lemma
(ensures
forall (y: a).
FStar.Seq.Properties.contains (FStar.Seq.Properties.snoc s x) y <==>
FStar.Seq.Properties.contains s y \/ x == y) | {
"end_col": 73,
"end_line": 463,
"start_col": 2,
"start_line": 463
} |
FStar.Pervasives.Lemma | val lemma_mem_count' (#a: eqtype) (s: seq a) (f: (a -> Tot bool))
: Lemma (requires (forall (i: nat{i < length s}). f (index s i)))
(ensures (forall (x: a). mem x s ==> f x))
(decreases (length s)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec lemma_mem_count' (#a:eqtype) (s:seq a) (f:a -> Tot bool)
: Lemma
(requires (forall (i:nat{i<length s}). f (index s i)))
(ensures (forall (x:a). mem x s ==> f x))
(decreases (length s))
= if length s = 0
then ()
else (let t = i:nat{i<length (tail s)} in
cut (forall (i:t). index (tail s) i = ind... | val lemma_mem_count' (#a: eqtype) (s: seq a) (f: (a -> Tot bool))
: Lemma (requires (forall (i: nat{i < length s}). f (index s i)))
(ensures (forall (x: a). mem x s ==> f x))
(decreases (length s))
let rec lemma_mem_count' (#a: eqtype) (s: seq a) (f: (a -> Tot bool))
: Lemma (requires (forall (i: na... | false | null | true | if length s = 0
then ()
else
(let t = i: nat{i < length (tail s)} in
cut (forall (i: t). index (tail s) i = index s (i + 1));
lemma_mem_count' (tail s) f) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.bool",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_mem_count'",
"FStar.Seq.Properties.tail",
"Prims.unit",
"Prims.cut",
"Prims.l_Forall",
"Prims.b2t",
"FStar.Seq.Base.index",
"Prims.op_Addition",
"Pri... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_mem_count' (#a: eqtype) (s: seq a) (f: (a -> Tot bool))
: Lemma (requires (forall (i: nat{i < length s}). f (index s i)))
(ensures (forall (x: a). mem x s ==> f x))
(decreases (length s)) | [
"recursion"
] | FStar.Seq.Properties.lemma_mem_count' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma
(requires forall (i: Prims.nat{i < FStar.Seq.Base.length s}). f (FStar.Seq.Base.index s i))
(ensures forall (x: a). FStar.Seq.Properties.mem x s ==> f x)
(decreases FStar.Seq.Base.length s) | {
"end_col": 36,
"end_line": 123,
"start_col": 2,
"start_line": 119
} |
FStar.Pervasives.Lemma | val lemma_seq_to_list_permutation' (#a: eqtype) (s: seq a)
: Lemma (requires True)
(ensures (forall x. count x s == List.Tot.Base.count x (seq_to_list s)))
(decreases (length s)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "F... | false | let rec lemma_seq_to_list_permutation' (#a:eqtype) (s:seq a)
:Lemma (requires True) (ensures (forall x. count x s == List.Tot.Base.count x (seq_to_list s))) (decreases (length s))
= if length s > 0 then lemma_seq_to_list_permutation' (slice s 1 (length s)) | val lemma_seq_to_list_permutation' (#a: eqtype) (s: seq a)
: Lemma (requires True)
(ensures (forall x. count x s == List.Tot.Base.count x (seq_to_list s)))
(decreases (length s))
let rec lemma_seq_to_list_permutation' (#a: eqtype) (s: seq a)
: Lemma (requires True)
(ensures (forall x. count x ... | false | null | true | if length s > 0 then lemma_seq_to_list_permutation' (slice s 1 (length s)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.op_GreaterThan",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_seq_to_list_permutation'",
"FStar.Seq.Base.slice",
"Prims.bool",
"Prims.unit",
"Prims.l_True",
"Prims.squash",
"Prims.l_Forall",
"Prims.eq2",
"Prims.nat",
"FStar.Seq.Propertie... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_to_list_permutation' (#a: eqtype) (s: seq a)
: Lemma (requires True)
(ensures (forall x. count x s == List.Tot.Base.count x (seq_to_list s)))
(decreases (length s)) | [
"recursion"
] | FStar.Seq.Properties.lemma_seq_to_list_permutation' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.count x s ==
FStar.List.Tot.Base.count x (FStar.Seq.Properties.seq_to_list s))
(decreases FStar.Seq.Base.length s) | {
"end_col": 78,
"end_line": 596,
"start_col": 4,
"start_line": 596
} |
FStar.Pervasives.Lemma | val un_snoc_snoc (#a:Type) (s:seq a) (x:a) : Lemma (un_snoc (snoc s x) == (s, x)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let un_snoc_snoc #_ s x =
let s', x = un_snoc (snoc s x) in
assert (Seq.equal s s') | val un_snoc_snoc (#a:Type) (s:seq a) (x:a) : Lemma (un_snoc (snoc s x) == (s, x))
let un_snoc_snoc #_ s x = | false | null | true | let s', x = un_snoc (snoc s x) in
assert (Seq.equal s s') | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims._assert",
"FStar.Seq.Base.equal",
"Prims.unit",
"FStar.Pervasives.Native.tuple2",
"Prims.eq2",
"FStar.Seq.Properties.snoc",
"FStar.Pervasives.Native.fst",
"FStar.Pervasives.Native.snd",
"FStar.Seq.Properties.un_snoc"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val un_snoc_snoc (#a:Type) (s:seq a) (x:a) : Lemma (un_snoc (snoc s x) == (s, x)) | [] | FStar.Seq.Properties.un_snoc_snoc | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> x: a
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.un_snoc (FStar.Seq.Properties.snoc s x) ==
FStar.Pervasives.Native.Mktuple2 s x) | {
"end_col": 25,
"end_line": 367,
"start_col": 25,
"start_line": 365
} |
FStar.Pervasives.Lemma | val lemma_append_inj_l: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a{length s1 = length t1 /\ equal (append s1 s2) (append t1 t2)} -> i:nat{i < length s1}
-> Lemma (index s1 i == index t1 i) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_append_inj_l #_ s1 s2 t1 t2 i =
assert (index s1 i == (index (append s1 s2) i));
assert (index t1 i == (index (append t1 t2) i)) | val lemma_append_inj_l: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a{length s1 = length t1 /\ equal (append s1 s2) (append t1 t2)} -> i:nat{i < length s1}
-> Lemma (index s1 i == index t1 i)
let lemma_append_inj_l #_ s1 s2 t1 t2 i = | false | null | true | assert (index s1 i == (index (append s1 s2) i));
assert (index t1 i == (index (append t1 t2) i)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.l_and",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append",
"Prims.op_LessThan",
"Prims._assert",
"Prims.eq2",
"FStar.Seq.Base.index",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_append_inj_l: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a{length s1 = length t1 /\ equal (append s1 s2) (append t1 t2)} -> i:nat{i < length s1}
-> Lemma (index s1 i == index t1 i) | [] | FStar.Seq.Properties.lemma_append_inj_l | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a ->
t1: FStar.Seq.Base.seq a ->
t2:
FStar.Seq.Base.seq a
{ FStar.Seq.Base.length s1 = FStar.Seq.Base.length t1 /\
FStar.Seq.Base.equal (FStar.Seq.Base.append s1 s2) (FStar.Seq.Base.append t1 t2) } ->
i: Prims.nat{i < FStar.... | {
"end_col": 49,
"end_line": 24,
"start_col": 2,
"start_line": 23
} |
FStar.Pervasives.Lemma | val intro_append_contains_from_disjunction (#a: Type) (s1 s2: seq a) (x: a)
: Lemma (requires s1 `contains` x \/ s2 `contains` x) (ensures (append s1 s2) `contains` x) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "F... | false | let intro_append_contains_from_disjunction (#a:Type) (s1:seq a) (s2:seq a) (x:a)
: Lemma (requires s1 `contains` x \/ s2 `contains` x)
(ensures (append s1 s2) `contains` x)
= let open FStar.Classical in
let open FStar.Squash in
or_elim #(s1 `contains` x) #(s2 `contains` x) #(fun _ -> (ap... | val intro_append_contains_from_disjunction (#a: Type) (s1 s2: seq a) (x: a)
: Lemma (requires s1 `contains` x \/ s2 `contains` x) (ensures (append s1 s2) `contains` x)
let intro_append_contains_from_disjunction (#a: Type) (s1 s2: seq a) (x: a)
: Lemma (requires s1 `contains` x \/ s2 `contains` x) (ensures (appe... | false | null | true | let open FStar.Classical in
let open FStar.Squash in
or_elim #(s1 `contains` x)
#(s2 `contains` x)
#(fun _ -> (append s1 s2) `contains` x)
(fun _ -> ())
(fun _ ->
let s = append s1 s2 in
exists_elim (s `contains` x)
(get_proof (s2 `contains` x))
(fun k -> assert (Seq.index s (Seq.len... | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"FStar.Classical.or_elim",
"FStar.Seq.Properties.contains",
"Prims.squash",
"Prims.l_or",
"FStar.Seq.Base.append",
"Prims.unit",
"FStar.Classical.exists_elim",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.eq2",
"FStar... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val intro_append_contains_from_disjunction (#a: Type) (s1 s2: seq a) (x: a)
: Lemma (requires s1 `contains` x \/ s2 `contains` x) (ensures (append s1 s2) `contains` x) | [] | FStar.Seq.Properties.intro_append_contains_from_disjunction | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> x: a
-> FStar.Pervasives.Lemma
(requires FStar.Seq.Properties.contains s1 x \/ FStar.Seq.Properties.contains s2 x)
(ensures FStar.Seq.Properties.contains (FStar.Seq.Base.append s1 s2) x) | {
"end_col": 62,
"end_line": 457,
"start_col": 6,
"start_line": 451
} |
FStar.Pervasives.Lemma | val find_mem (#a:eqtype) (s:seq a) (f:a -> Tot bool) (x:a{f x})
: Lemma (requires (mem x s))
(ensures (Some? (seq_find f s) /\ f (Some?.v (seq_find f s)))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let find_mem #_ s f x
= match seq_find f s with
| None -> mem_index x s
| Some _ -> () | val find_mem (#a:eqtype) (s:seq a) (f:a -> Tot bool) (x:a{f x})
: Lemma (requires (mem x s))
(ensures (Some? (seq_find f s) /\ f (Some?.v (seq_find f s))))
let find_mem #_ s f x = | false | null | true | match seq_find f s with
| None -> mem_index x s
| Some _ -> () | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.bool",
"Prims.b2t",
"FStar.Seq.Properties.seq_find",
"FStar.Seq.Properties.mem_index",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_mem (#a:eqtype) (s:seq a) (f:a -> Tot bool) (x:a{f x})
: Lemma (requires (mem x s))
(ensures (Some? (seq_find f s) /\ f (Some?.v (seq_find f s)))) | [] | FStar.Seq.Properties.find_mem | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool) -> x: a{f x}
-> FStar.Pervasives.Lemma (requires FStar.Seq.Properties.mem x s)
(ensures
Some? (FStar.Seq.Properties.seq_find f s) /\ f (Some?.v (FStar.Seq.Properties.seq_find f s))
) | {
"end_col": 19,
"end_line": 372,
"start_col": 5,
"start_line": 370
} |
FStar.Pervasives.Lemma | val swap_frame_hi : #a:Type -> s:seq a -> i:nat -> j:nat{i <= j} -> k:nat{j < k} -> hi:nat{k <= hi /\ hi <= length s}
-> Lemma (ensures (slice s k hi == slice (swap s i j) k hi)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let swap_frame_hi #_ s i j k hi = cut (equal (slice s k hi) (slice (swap s i j) k hi)) | val swap_frame_hi : #a:Type -> s:seq a -> i:nat -> j:nat{i <= j} -> k:nat{j < k} -> hi:nat{k <= hi /\ hi <= length s}
-> Lemma (ensures (slice s k hi == slice (swap s i j) k hi))
let swap_frame_hi #_ s i j k hi = | false | null | true | cut (equal (slice s k hi) (slice (swap s i j) k hi)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_LessThan",
"Prims.l_and",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.slice",
"FStar.Seq.Properties.swap",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val swap_frame_hi : #a:Type -> s:seq a -> i:nat -> j:nat{i <= j} -> k:nat{j < k} -> hi:nat{k <= hi /\ hi <= length s}
-> Lemma (ensures (slice s k hi == slice (swap s i j) k hi)) | [] | FStar.Seq.Properties.swap_frame_hi | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
i: Prims.nat ->
j: Prims.nat{i <= j} ->
k: Prims.nat{j < k} ->
hi: Prims.nat{k <= hi /\ hi <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Base.slice s k hi == FStar.Seq.Base.slice (FStar.Seq.Properties.swap s i j) k hi) | {
"end_col": 86,
"end_line": 264,
"start_col": 34,
"start_line": 264
} |
FStar.Pervasives.Lemma | val lemma_seq_frame_hi: #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat{i <= j} -> m:nat{j <= m} -> n:nat{m < n && n <= length s1}
-> Lemma
(requires (s1 == (splice s2 i s1 j)))
(ensures ((slice s1 m n == slice s2 m n) /\ (index s1 m == index s2 m))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_seq_frame_hi #_ s1 s2 i j m n =
cut (equal (slice s1 m n) (slice s2 m n)) | val lemma_seq_frame_hi: #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat{i <= j} -> m:nat{j <= m} -> n:nat{m < n && n <= length s1}
-> Lemma
(requires (s1 == (splice s2 i s1 j)))
(ensures ((slice s1 m n == slice s2 m n) /\ (index s1 m == index s2 m)))
let lemma_seq_frame_hi #_ s1 s2 i j m... | false | null | true | cut (equal (slice s1 m n) (slice s2 m n)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"Prims.op_LessThanOrEqual",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.slice",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_frame_hi: #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat{i <= j} -> m:nat{j <= m} -> n:nat{m < n && n <= length s1}
-> Lemma
(requires (s1 == (splice s2 i s1 j)))
(ensures ((slice s1 m n == slice s2 m n) /\ (index s1 m == index s2 m))) | [] | FStar.Seq.Properties.lemma_seq_frame_hi | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a {FStar.Seq.Base.length s1 = FStar.Seq.Base.length s2} ->
i: Prims.nat ->
j: Prims.nat{i <= j} ->
m: Prims.nat{j <= m} ->
n: Prims.nat{m < n && n <= FStar.Seq.Base.length s1}
-> FStar.Pervasives.Lemma (requires s1 == FStar.Seq.Properties.spl... | {
"end_col": 43,
"end_line": 278,
"start_col": 2,
"start_line": 278
} |
FStar.Pervasives.Lemma | val mem_cons
(#a:eqtype)
(x:a)
(s:seq a)
: Lemma
(ensures (forall y. mem y (cons x s) <==> mem y s \/ x=y)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let mem_cons #_ x s = lemma_append_count (create 1 x) s | val mem_cons
(#a:eqtype)
(x:a)
(s:seq a)
: Lemma
(ensures (forall y. mem y (cons x s) <==> mem y s \/ x=y))
let mem_cons #_ x s = | false | null | true | lemma_append_count (create 1 x) s | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"FStar.Seq.Properties.lemma_append_count",
"FStar.Seq.Base.create",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val mem_cons
(#a:eqtype)
(x:a)
(s:seq a)
: Lemma
(ensures (forall y. mem y (cons x s) <==> mem y s \/ x=y)) | [] | FStar.Seq.Properties.mem_cons | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: a -> s: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
forall (y: a).
FStar.Seq.Properties.mem y (FStar.Seq.Properties.cons x s) <==>
FStar.Seq.Properties.mem y s \/ x = y) | {
"end_col": 55,
"end_line": 515,
"start_col": 22,
"start_line": 515
} |
FStar.Pervasives.Lemma | val seq_of_list_tl
(#a: Type)
(l: list a { List.Tot.length l > 0 } )
: Lemma
(requires True)
(ensures (seq_of_list (List.Tot.tl l) == tail (seq_of_list l))) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let seq_of_list_tl #_ l = lemma_seq_of_list_induction l | val seq_of_list_tl
(#a: Type)
(l: list a { List.Tot.length l > 0 } )
: Lemma
(requires True)
(ensures (seq_of_list (List.Tot.tl l) == tail (seq_of_list l)))
let seq_of_list_tl #_ l = | false | null | true | lemma_seq_of_list_induction l | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.list",
"Prims.b2t",
"Prims.op_GreaterThan",
"FStar.List.Tot.Base.length",
"FStar.Seq.Properties.lemma_seq_of_list_induction",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val seq_of_list_tl
(#a: Type)
(l: list a { List.Tot.length l > 0 } )
: Lemma
(requires True)
(ensures (seq_of_list (List.Tot.tl l) == tail (seq_of_list l))) | [] | FStar.Seq.Properties.seq_of_list_tl | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a {FStar.List.Tot.Base.length l > 0}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.seq_of_list (FStar.List.Tot.Base.tl l) ==
FStar.Seq.Properties.tail (FStar.Seq.Properties.seq_of_list l)) | {
"end_col": 55,
"end_line": 533,
"start_col": 26,
"start_line": 533
} |
FStar.Pervasives.Lemma | val suffix_of_tail
(#a: Type)
(s: seq a {length s > 0})
: Lemma
(requires True)
(ensures ((tail s) `suffix_of` s))
[SMTPat ((tail s) `suffix_of` s)] | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let suffix_of_tail #_ s = cons_head_tail s | val suffix_of_tail
(#a: Type)
(s: seq a {length s > 0})
: Lemma
(requires True)
(ensures ((tail s) `suffix_of` s))
[SMTPat ((tail s) `suffix_of` s)]
let suffix_of_tail #_ s = | false | null | true | cons_head_tail s | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_GreaterThan",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.cons_head_tail",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val suffix_of_tail
(#a: Type)
(s: seq a {length s > 0})
: Lemma
(requires True)
(ensures ((tail s) `suffix_of` s))
[SMTPat ((tail s) `suffix_of` s)] | [] | FStar.Seq.Properties.suffix_of_tail | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a {FStar.Seq.Base.length s > 0}
-> FStar.Pervasives.Lemma (ensures FStar.Seq.Properties.suffix_of (FStar.Seq.Properties.tail s) s)
[SMTPat (FStar.Seq.Properties.suffix_of (FStar.Seq.Properties.tail s) s)] | {
"end_col": 42,
"end_line": 505,
"start_col": 26,
"start_line": 505
} |
FStar.Pervasives.Lemma | val lemma_slice_cons: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s i || mem x (slice s (i + 1) j)))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_slice_cons #_ s i j =
cut (equal (slice s i j) (append (create 1 (index s i)) (slice s (i + 1) j)));
lemma_mem_append (create 1 (index s i)) (slice s (i + 1) j) | val lemma_slice_cons: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s i || mem x (slice s (i + 1) j))))
let lemma_slice_cons #_ s i j = | false | null | true | cut (equal (slice s i j) (append (create 1 (index s i)) (slice s (i + 1) j)));
lemma_mem_append (create 1 (index s i)) (slice s (i + 1) j) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_mem_append",
"FStar.Seq.Base.create",
"FStar.Seq.Base.index",
"FStar.Seq.Base.slice",
"Prims.op_Addition",
... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_slice_cons: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s i || mem x (slice s (i + 1) j)))) | [] | FStar.Seq.Properties.lemma_slice_cons | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat -> j: Prims.nat{i < j && j <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.mem x (FStar.Seq.Base.slice s i j) <==>
x = FStar.Seq.Base.index s i ||
FStar.Seq.Properties.mem x (FStar.Seq.Base.sli... | {
"end_col": 61,
"end_line": 246,
"start_col": 2,
"start_line": 245
} |
FStar.Pervasives.Lemma | val lemma_weaken_frame_left : #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j && j <= k && k <= length s1}
-> Lemma
(requires (s1 == splice s2 j s1 k))
(ensures (s1 == splice s2 i s1 k)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_weaken_frame_left #_ s1 s2 i j k = cut (equal s1 (splice s2 i s1 k)) | val lemma_weaken_frame_left : #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j && j <= k && k <= length s1}
-> Lemma
(requires (s1 == splice s2 j s1 k))
(ensures (s1 == splice s2 i s1 k))
let lemma_weaken_frame_left #_ s1 s2 i j k = | false | null | true | cut (equal s1 (splice s2 i s1 k)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.splice",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_weaken_frame_left : #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j && j <= k && k <= length s1}
-> Lemma
(requires (s1 == splice s2 j s1 k))
(ensures (s1 == splice s2 i s1 k)) | [] | FStar.Seq.Properties.lemma_weaken_frame_left | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a {FStar.Seq.Base.length s1 = FStar.Seq.Base.length s2} ->
i: Prims.nat ->
j: Prims.nat ->
k: Prims.nat{i <= j && j <= k && k <= FStar.Seq.Base.length s1}
-> FStar.Pervasives.Lemma (requires s1 == FStar.Seq.Properties.splice s2 j s1 k)
(ens... | {
"end_col": 78,
"end_line": 288,
"start_col": 45,
"start_line": 288
} |
FStar.Pervasives.Lemma | val snoc_slice_index
(#a: Type)
(s: seq a)
(i: nat)
(j: nat {i <= j /\ j < length s} )
: Lemma
(requires True)
(ensures (snoc (slice s i j) (index s j) == slice s i (j + 1)))
[SMTPat (snoc (slice s i j) (index s j))] | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let snoc_slice_index #_ s i j = lemma_eq_elim (snoc (slice s i j) (index s j)) (slice s i (j + 1)) | val snoc_slice_index
(#a: Type)
(s: seq a)
(i: nat)
(j: nat {i <= j /\ j < length s} )
: Lemma
(requires True)
(ensures (snoc (slice s i j) (index s j) == slice s i (j + 1)))
[SMTPat (snoc (slice s i j) (index s j))]
let snoc_slice_index #_ s i j = | false | null | true | lemma_eq_elim (snoc (slice s i j) (index s j)) (slice s i (j + 1)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"FStar.Seq.Base.lemma_eq_elim",
"FStar.Seq.Properties.snoc",
"FStar.Seq.Base.slice",
"FStar.Seq.Base.index",
"Prims.op_Addition",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val snoc_slice_index
(#a: Type)
(s: seq a)
(i: nat)
(j: nat {i <= j /\ j < length s} )
: Lemma
(requires True)
(ensures (snoc (slice s i j) (index s j) == slice s i (j + 1)))
[SMTPat (snoc (slice s i j) (index s j))] | [] | FStar.Seq.Properties.snoc_slice_index | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat -> j: Prims.nat{i <= j /\ j < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.snoc (FStar.Seq.Base.slice s i j) (FStar.Seq.Base.index s j) ==
FStar.Seq.Base.slice s i (j + 1))
[SMTPat (FStar.Seq.Properties.snoc (FStar... | {
"end_col": 98,
"end_line": 517,
"start_col": 32,
"start_line": 517
} |
FStar.Pervasives.Lemma | val elim_of_list (#a: Type) (l: list a):
Lemma
(ensures (
let s = seq_of_list l in
pointwise_and s l)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let elim_of_list #_ l = elim_of_list' 0 (seq_of_list l) l | val elim_of_list (#a: Type) (l: list a):
Lemma
(ensures (
let s = seq_of_list l in
pointwise_and s l))
let elim_of_list #_ l = | false | null | true | elim_of_list' 0 (seq_of_list l) l | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.list",
"FStar.Seq.Properties.elim_of_list'",
"FStar.Seq.Properties.seq_of_list",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val elim_of_list (#a: Type) (l: list a):
Lemma
(ensures (
let s = seq_of_list l in
pointwise_and s l)) | [] | FStar.Seq.Properties.elim_of_list | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a
-> FStar.Pervasives.Lemma
(ensures
(let s = FStar.Seq.Properties.seq_of_list l in
FStar.Seq.Properties.pointwise_and s l)) | {
"end_col": 57,
"end_line": 592,
"start_col": 24,
"start_line": 592
} |
FStar.Pervasives.Lemma | val lemma_append_count' (#a: eqtype) (lo hi: seq a)
: Lemma (requires True)
(ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))
(decreases (length lo)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec lemma_append_count' (#a:eqtype) (lo:seq a) (hi:seq a)
: Lemma
(requires True)
(ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))
(decreases (length lo))
= if length lo = 0
then cut (equal (append lo hi) hi)
else (cut (equal (cons (head lo) (append (tail lo) hi))
(... | val lemma_append_count' (#a: eqtype) (lo hi: seq a)
: Lemma (requires True)
(ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))
(decreases (length lo))
let rec lemma_append_count' (#a: eqtype) (lo hi: seq a)
: Lemma (requires True)
(ensures (forall x. count x (append lo hi... | false | null | true | if length lo = 0
then cut (equal (append lo hi) hi)
else
(cut (equal (cons (head lo) (append (tail lo) hi)) (append lo hi));
lemma_append_count' (tail lo) hi;
let tl_l_h = append (tail lo) hi in
let lh = cons (head lo) tl_l_h in
cut (equal (tail lh) tl_l_h)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append",
"Prims.bool",
"FStar.Seq.Properties.tail",
"FStar.Seq.Properties.cons",
"FStar.Seq.Properties.head",
"Prims.unit",
"FStar.Seq.Prope... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_append_count' (#a: eqtype) (lo hi: seq a)
: Lemma (requires True)
(ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))
(decreases (length lo)) | [
"recursion"
] | FStar.Seq.Properties.lemma_append_count' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | lo: FStar.Seq.Base.seq a -> hi: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.count x (FStar.Seq.Base.append lo hi) =
FStar.Seq.Properties.count x lo + FStar.Seq.Properties.count x hi)
(decreases FStar.Seq.Base.length lo) | {
"end_col": 37,
"end_line": 106,
"start_col": 2,
"start_line": 99
} |
FStar.Pervasives.Lemma | val lemma_seq_list_bij' (#a: Type) (s: seq a)
: Lemma (requires (True)) (ensures (seq_of_list (seq_to_list s) == s)) (decreases (length s)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "F... | false | let rec lemma_seq_list_bij': #a:Type -> s:seq a -> Lemma
(requires (True))
(ensures (seq_of_list (seq_to_list s) == s))
(decreases (length s))
= fun #_ s ->
let l = seq_to_list s in
lemma_seq_of_list_induction l;
if length s = 0 then (
assert (equal s (seq_of_list l))
)
else (
lemma_seq_list_bi... | val lemma_seq_list_bij' (#a: Type) (s: seq a)
: Lemma (requires (True)) (ensures (seq_of_list (seq_to_list s) == s)) (decreases (length s))
let rec lemma_seq_list_bij': #a: Type -> s: seq a
-> Lemma (requires (True)) (ensures (seq_of_list (seq_to_list s) == s)) (decreases (length s)) = | false | null | true | fun #_ s ->
let l = seq_to_list s in
lemma_seq_of_list_induction l;
if length s = 0
then (assert (equal s (seq_of_list l)))
else
(lemma_seq_list_bij' (slice s 1 (length s));
assert (equal s (seq_of_list (seq_to_list s)))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Base.seq",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"Prims._assert",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.seq_of_list",
"Prims.bool",
"FStar.Seq.Properties.seq_to_list",
"Prims.unit",
"FStar.Seq.Properties.lemma_seq_list_bij'",
"FStar.Seq.Base.slice",
"F... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_list_bij' (#a: Type) (s: seq a)
: Lemma (requires (True)) (ensures (seq_of_list (seq_to_list s) == s)) (decreases (length s)) | [
"recursion"
] | FStar.Seq.Properties.lemma_seq_list_bij' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures FStar.Seq.Properties.seq_of_list (FStar.Seq.Properties.seq_to_list s) == s)
(decreases FStar.Seq.Base.length s) | {
"end_col": 3,
"end_line": 407,
"start_col": 2,
"start_line": 398
} |
FStar.Pervasives.Lemma | val lemma_seq_of_list_permutation (#a:eqtype) (l:list a)
:Lemma (forall x. List.Tot.Base.count x l == count x (seq_of_list l)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let rec lemma_seq_of_list_permutation #a l
=
lemma_seq_of_list_induction l;
match l with
| [] -> ()
| _::tl -> lemma_seq_of_list_permutation tl | val lemma_seq_of_list_permutation (#a:eqtype) (l:list a)
:Lemma (forall x. List.Tot.Base.count x l == count x (seq_of_list l))
let rec lemma_seq_of_list_permutation #a l = | false | null | true | lemma_seq_of_list_induction l;
match l with
| [] -> ()
| _ :: tl -> lemma_seq_of_list_permutation tl | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"Prims.list",
"FStar.Seq.Properties.lemma_seq_of_list_permutation",
"Prims.unit",
"FStar.Seq.Properties.lemma_seq_of_list_induction"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_of_list_permutation (#a:eqtype) (l:list a)
:Lemma (forall x. List.Tot.Base.count x l == count x (seq_of_list l)) | [
"recursion"
] | FStar.Seq.Properties.lemma_seq_of_list_permutation | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.List.Tot.Base.count x l ==
FStar.Seq.Properties.count x (FStar.Seq.Properties.seq_of_list l)) | {
"end_col": 47,
"end_line": 605,
"start_col": 4,
"start_line": 602
} |
FStar.Pervasives.Lemma | val find_append_none' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (None? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s2))
(decreases (length s1)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec find_append_none': #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s2))
(decreases (length s1))
= fun #_ s1 s2 f ->
if Seq.length s1 = 0 then cut (equal (append s1 s2) s2)
else
let _ = cut (equal (tail (ap... | val find_append_none' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (None? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s2))
(decreases (length s1))
let rec find_append_none': #a: Type -> s1: seq a -> s2: seq a -> f: (a -> Tot bool)
-> Lemma (requires (None? (find_l... | false | null | true | fun #_ s1 s2 f ->
if Seq.length s1 = 0
then cut (equal (append s1 s2) s2)
else
let _ = cut (equal (tail (append s1 s2)) (append (tail s1) s2)) in
find_append_none' (tail s1) s2 f | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Base.seq",
"Prims.bool",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append",
"FStar.Seq.Properties.find_append_none'",
"FStar.Seq.Properties.tail",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_append_none' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (None? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s2))
(decreases (length s1)) | [
"recursion"
] | FStar.Seq.Properties.find_append_none' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma (requires None? (FStar.Seq.Properties.find_l f s1))
(ensures
FStar.Seq.Properties.find_l f (FStar.Seq.Base.append s1 s2) ==
FStar.Seq.Properties.find_l f s2)
(decreases FStar.Seq.Base.... | {
"end_col": 36,
"end_line": 343,
"start_col": 2,
"start_line": 339
} |
FStar.Pervasives.Lemma | val lemma_index_is_nth' (#a: Type) (s: seq a) (i: nat{i < length s})
: Lemma (requires True) (ensures (L.index (seq_to_list s) i == index s i)) (decreases i) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "F... | false | let rec lemma_index_is_nth': #a:Type -> s:seq a -> i:nat{i < length s} -> Lemma
(requires True)
(ensures (L.index (seq_to_list s) i == index s i))
(decreases i)
= fun #_ s i ->
if i = 0 then ()
else (
lemma_index_is_nth' (slice s 1 (length s)) (i-1)
) | val lemma_index_is_nth' (#a: Type) (s: seq a) (i: nat{i < length s})
: Lemma (requires True) (ensures (L.index (seq_to_list s) i == index s i)) (decreases i)
let rec lemma_index_is_nth': #a: Type -> s: seq a -> i: nat{i < length s}
-> Lemma (requires True) (ensures (L.index (seq_to_list s) i == index s i)) (decre... | false | null | true | fun #_ s i -> if i = 0 then () else (lemma_index_is_nth' (slice s 1 (length s)) (i - 1)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.op_Equality",
"Prims.int",
"Prims.bool",
"FStar.Seq.Properties.lemma_index_is_nth'",
"FStar.Seq.Base.slice",
"Prims.op_Subtraction",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_index_is_nth' (#a: Type) (s: seq a) (i: nat{i < length s})
: Lemma (requires True) (ensures (L.index (seq_to_list s) i == index s i)) (decreases i) | [
"recursion"
] | FStar.Seq.Properties.lemma_index_is_nth' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat{i < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.List.Tot.Base.index (FStar.Seq.Properties.seq_to_list s) i == FStar.Seq.Base.index s i
) (decreases i) | {
"end_col": 3,
"end_line": 433,
"start_col": 2,
"start_line": 429
} |
FStar.Pervasives.Lemma | val cons_head_tail
(#a: Type)
(s: seq a {length s > 0})
: Lemma
(requires True)
(ensures (s == cons (head s) (tail s)))
[SMTPat (cons (head s) (tail s))] | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let cons_head_tail #_ s =
let _ : squash (slice s 0 1 == create 1 (index s 0)) =
lemma_index_slice s 0 1 0;
lemma_index_create 1 (index s 0) 0;
lemma_eq_elim (slice s 0 1) (create 1 (index s 0))
in
lemma_split s 1 | val cons_head_tail
(#a: Type)
(s: seq a {length s > 0})
: Lemma
(requires True)
(ensures (s == cons (head s) (tail s)))
[SMTPat (cons (head s) (tail s))]
let cons_head_tail #_ s = | false | null | true | let _:squash (slice s 0 1 == create 1 (index s 0)) =
lemma_index_slice s 0 1 0;
lemma_index_create 1 (index s 0) 0;
lemma_eq_elim (slice s 0 1) (create 1 (index s 0))
in
lemma_split s 1 | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_GreaterThan",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_split",
"Prims.squash",
"Prims.eq2",
"FStar.Seq.Base.slice",
"FStar.Seq.Base.create",
"FStar.Seq.Base.index",
"FStar.Seq.Base.lemma_eq_elim",
"Prims.unit",
"FStar.Seq.Base.lemma_in... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val cons_head_tail
(#a: Type)
(s: seq a {length s > 0})
: Lemma
(requires True)
(ensures (s == cons (head s) (tail s)))
[SMTPat (cons (head s) (tail s))] | [] | FStar.Seq.Properties.cons_head_tail | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a {FStar.Seq.Base.length s > 0}
-> FStar.Pervasives.Lemma
(ensures
s == FStar.Seq.Properties.cons (FStar.Seq.Properties.head s) (FStar.Seq.Properties.tail s))
[
SMTPat (FStar.Seq.Properties.cons (FStar.Seq.Properties.head s)
(FStar.Seq.Properties.tail s)... | {
"end_col": 17,
"end_line": 501,
"start_col": 25,
"start_line": 495
} |
FStar.Pervasives.Lemma | val lemma_seq_of_list_sorted (#a:Type) (f:a -> a -> Tot bool) (l:list a)
:Lemma (requires (List.Tot.Properties.sorted f l)) (ensures (sorted f (seq_of_list l))) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let rec lemma_seq_of_list_sorted #a f l
=
lemma_seq_of_list_induction l;
if List.Tot.length l > 1 then begin
lemma_seq_of_list_induction (List.Tot.Base.tl l);
lemma_seq_of_list_sorted f (List.Tot.Base.tl l)
end | val lemma_seq_of_list_sorted (#a:Type) (f:a -> a -> Tot bool) (l:list a)
:Lemma (requires (List.Tot.Properties.sorted f l)) (ensures (sorted f (seq_of_list l)))
let rec lemma_seq_of_list_sorted #a f l = | false | null | true | lemma_seq_of_list_induction l;
if List.Tot.length l > 1
then
(lemma_seq_of_list_induction (List.Tot.Base.tl l);
lemma_seq_of_list_sorted f (List.Tot.Base.tl l)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.bool",
"Prims.list",
"Prims.op_GreaterThan",
"FStar.List.Tot.Base.length",
"FStar.Seq.Properties.lemma_seq_of_list_sorted",
"FStar.List.Tot.Base.tl",
"Prims.unit",
"FStar.Seq.Properties.lemma_seq_of_list_induction"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_of_list_sorted (#a:Type) (f:a -> a -> Tot bool) (l:list a)
:Lemma (requires (List.Tot.Properties.sorted f l)) (ensures (sorted f (seq_of_list l))) | [
"recursion"
] | FStar.Seq.Properties.lemma_seq_of_list_sorted | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | f: (_: a -> _: a -> Prims.bool) -> l: Prims.list a
-> FStar.Pervasives.Lemma (requires FStar.List.Tot.Properties.sorted f l)
(ensures FStar.Seq.Properties.sorted f (FStar.Seq.Properties.seq_of_list l)) | {
"end_col": 7,
"end_line": 613,
"start_col": 4,
"start_line": 609
} |
FStar.Pervasives.Lemma | val intro_of_list'' (#a: Type) (i: nat) (s: seq a) (l: list a)
: Lemma (requires (List.Tot.length l + i = length s /\ i <= length s /\ explode_and i s l))
(ensures (equal (seq_of_list l) (slice s i (length s))))
(decreases (List.Tot.length l)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "F... | false | let rec intro_of_list'': #a:Type ->
i:nat ->
s:seq a ->
l:list a ->
Lemma
(requires (
List.Tot.length l + i = length s /\
i <= length s /\
explode_and i s l))
(ensures (
equal (seq_of_list l) (slice s i (length s))))
(decreases (
List.Tot.length l))
= fun #_ i s l ->
... | val intro_of_list'' (#a: Type) (i: nat) (s: seq a) (l: list a)
: Lemma (requires (List.Tot.length l + i = length s /\ i <= length s /\ explode_and i s l))
(ensures (equal (seq_of_list l) (slice s i (length s))))
(decreases (List.Tot.length l))
let rec intro_of_list'': #a: Type -> i: nat -> s: seq a -> l... | false | null | true | fun #_ i s l ->
lemma_seq_of_list_induction l;
match l with
| [] -> ()
| hd :: tl -> intro_of_list'' (i + 1) s tl | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.nat",
"FStar.Seq.Base.seq",
"Prims.list",
"FStar.Seq.Properties.intro_of_list''",
"Prims.op_Addition",
"Prims.unit",
"FStar.Seq.Properties.lemma_seq_of_list_induction"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val intro_of_list'' (#a: Type) (i: nat) (s: seq a) (l: list a)
: Lemma (requires (List.Tot.length l + i = length s /\ i <= length s /\ explode_and i s l))
(ensures (equal (seq_of_list l) (slice s i (length s))))
(decreases (List.Tot.length l)) | [
"recursion"
] | FStar.Seq.Properties.intro_of_list'' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | i: Prims.nat -> s: FStar.Seq.Base.seq a -> l: Prims.list a
-> FStar.Pervasives.Lemma
(requires
FStar.List.Tot.Base.length l + i = FStar.Seq.Base.length s /\ i <= FStar.Seq.Base.length s /\
FStar.Seq.Properties.explode_and i s l)
(ensures
FStar.Seq.Base.equal (FStar.Seq.Properties.s... | {
"end_col": 44,
"end_line": 564,
"start_col": 2,
"start_line": 560
} |
FStar.Pervasives.Lemma | val lemma_weaken_perm_right: #a:eqtype -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j /\ j <= k /\ k <= length s1}
-> Lemma
(requires (s1 == splice s2 i s1 j /\ permutation a (slice s2 i j) (slice s1 i j)))
(ensures (permutation a (slice s2 i k) (slice s1 i k))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_weaken_perm_right #_ s1 s2 i j k =
cut (equal (slice s2 i k) (append (slice s2 i j)
(slice s2 j k)));
cut (equal (slice s1 i k) (append (slice s1 i j)
(slice s2 j k)));
lemma_append_count (slice s2 i j) (slice s2 j k);
lemma_append_coun... | val lemma_weaken_perm_right: #a:eqtype -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j /\ j <= k /\ k <= length s1}
-> Lemma
(requires (s1 == splice s2 i s1 j /\ permutation a (slice s2 i j) (slice s1 i j)))
(ensures (permutation a (slice s2 i k) (slice s1 i k)))
let lemma_weaken_... | false | null | true | cut (equal (slice s2 i k) (append (slice s2 i j) (slice s2 j k)));
cut (equal (slice s1 i k) (append (slice s1 i j) (slice s2 j k)));
lemma_append_count (slice s2 i j) (slice s2 j k);
lemma_append_count (slice s1 i j) (slice s2 j k) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"Prims.l_and",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Properties.lemma_append_count",
"FStar.Seq.Base.slice",
"Prims.unit",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.app... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_weaken_perm_right: #a:eqtype -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j /\ j <= k /\ k <= length s1}
-> Lemma
(requires (s1 == splice s2 i s1 j /\ permutation a (slice s2 i j) (slice s1 i j)))
(ensures (permutation a (slice s2 i k) (slice s1 i k))) | [] | FStar.Seq.Properties.lemma_weaken_perm_right | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a {FStar.Seq.Base.length s1 = FStar.Seq.Base.length s2} ->
i: Prims.nat ->
j: Prims.nat ->
k: Prims.nat{i <= j /\ j <= k /\ k <= FStar.Seq.Base.length s1}
-> FStar.Pervasives.Lemma
(requires
s1 == FStar.Seq.Properties.splice s2 i s1... | {
"end_col": 50,
"end_line": 306,
"start_col": 2,
"start_line": 301
} |
FStar.Pervasives.Lemma | val sorted_feq (#a:Type)
(f g : (a -> a -> Tot bool))
(s:seq a{forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let sorted_feq = sorted_feq' | val sorted_feq (#a:Type)
(f g : (a -> a -> Tot bool))
(s:seq a{forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s))
let sorted_feq = | false | null | true | sorted_feq' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.sorted_feq'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val sorted_feq (#a:Type)
(f g : (a -> a -> Tot bool))
(s:seq a{forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s)) | [] | FStar.Seq.Properties.sorted_feq | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
f: (_: a -> _: a -> Prims.bool) ->
g: (_: a -> _: a -> Prims.bool) ->
s: FStar.Seq.Base.seq a {forall (x: a) (y: a). f x y == g x y}
-> FStar.Pervasives.Lemma
(ensures FStar.Seq.Properties.sorted f s <==> FStar.Seq.Properties.sorted g s) | {
"end_col": 28,
"end_line": 92,
"start_col": 17,
"start_line": 92
} |
FStar.Pervasives.Lemma | val lemma_append_inj_r: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a{length s1 = length t1 /\ length s2 = length t2 /\ equal (append s1 s2) (append t1 t2)} -> i:nat{i < length s2}
-> Lemma (ensures (index s2 i == index t2 i)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_append_inj_r #_ s1 s2 t1 t2 i =
assert (index s2 i == (index (append s1 s2) (i + length s1)));
assert (index t2 i == (index (append t1 t2) (i + length t1))) | val lemma_append_inj_r: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a{length s1 = length t1 /\ length s2 = length t2 /\ equal (append s1 s2) (append t1 t2)} -> i:nat{i < length s2}
-> Lemma (ensures (index s2 i == index t2 i))
let lemma_append_inj_r #_ s1 s2 t1 t2 i = | false | null | true | assert (index s2 i == (index (append s1 s2) (i + length s1)));
assert (index t2 i == (index (append t1 t2) (i + length t1))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.l_and",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append",
"Prims.op_LessThan",
"Prims._assert",
"Prims.eq2",
"FStar.Seq.Base.index",
"Prims.op_Addition",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_append_inj_r: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a{length s1 = length t1 /\ length s2 = length t2 /\ equal (append s1 s2) (append t1 t2)} -> i:nat{i < length s2}
-> Lemma (ensures (index s2 i == index t2 i)) | [] | FStar.Seq.Properties.lemma_append_inj_r | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a ->
t1: FStar.Seq.Base.seq a ->
t2:
FStar.Seq.Base.seq a
{ FStar.Seq.Base.length s1 = FStar.Seq.Base.length t1 /\
FStar.Seq.Base.length s2 = FStar.Seq.Base.length t2 /\
FStar.Seq.Base.equal (FStar.Seq.Base.append s1 s... | {
"end_col": 63,
"end_line": 28,
"start_col": 2,
"start_line": 27
} |
FStar.Pervasives.Lemma | val lemma_append_count: #a:eqtype -> lo:seq a -> hi:seq a -> Lemma
(requires True)
(ensures (forall x. count x (append lo hi) = (count x lo + count x hi))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_append_count = lemma_append_count' | val lemma_append_count: #a:eqtype -> lo:seq a -> hi:seq a -> Lemma
(requires True)
(ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))
let lemma_append_count = | false | null | true | lemma_append_count' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.lemma_append_count'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_append_count: #a:eqtype -> lo:seq a -> hi:seq a -> Lemma
(requires True)
(ensures (forall x. count x (append lo hi) = (count x lo + count x hi))) | [] | FStar.Seq.Properties.lemma_append_count | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | lo: FStar.Seq.Base.seq a -> hi: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.count x (FStar.Seq.Base.append lo hi) =
FStar.Seq.Properties.count x lo + FStar.Seq.Properties.count x hi) | {
"end_col": 44,
"end_line": 108,
"start_col": 25,
"start_line": 108
} |
FStar.Pervasives.Lemma | val lemma_append_len_disj: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a {(length s1 = length t1 \/ length s2 = length t2) /\ (equal (append s1 s2) (append t1 t2))}
-> Lemma (ensures (length s1 = length t1 /\ length s2 = length t2)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_append_len_disj #_ s1 s2 t1 t2 =
cut (length (append s1 s2) == length s1 + length s2);
cut (length (append t1 t2) == length t1 + length t2) | val lemma_append_len_disj: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a {(length s1 = length t1 \/ length s2 = length t2) /\ (equal (append s1 s2) (append t1 t2))}
-> Lemma (ensures (length s1 = length t1 /\ length s2 = length t2))
let lemma_append_len_disj #_ s1 s2 t1 t2 = | false | null | true | cut (length (append s1 s2) == length s1 + length s2);
cut (length (append t1 t2) == length t1 + length t2) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.l_and",
"Prims.l_or",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append",
"Prims.cut",
"Prims.eq2",
"Prims.int",
"Prims.op_Addition",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_append_len_disj: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a {(length s1 = length t1 \/ length s2 = length t2) /\ (equal (append s1 s2) (append t1 t2))}
-> Lemma (ensures (length s1 = length t1 /\ length s2 = length t2)) | [] | FStar.Seq.Properties.lemma_append_len_disj | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a ->
t1: FStar.Seq.Base.seq a ->
t2:
FStar.Seq.Base.seq a
{ (FStar.Seq.Base.length s1 = FStar.Seq.Base.length t1 \/
FStar.Seq.Base.length s2 = FStar.Seq.Base.length t2) /\
FStar.Seq.Base.equal (FStar.Seq.Base.append ... | {
"end_col": 54,
"end_line": 32,
"start_col": 2,
"start_line": 31
} |
FStar.Pervasives.Lemma | val lemma_append_inj: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a {length s1 = length t1 \/ length s2 = length t2}
-> Lemma (requires (equal (append s1 s2) (append t1 t2)))
(ensures (equal s1 t1 /\ equal s2 t2)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_append_inj #_ s1 s2 t1 t2 =
lemma_append_len_disj s1 s2 t1 t2;
FStar.Classical.forall_intro #(i:nat{i < length s1}) #(fun i -> index s1 i == index t1 i) (lemma_append_inj_l s1 s2 t1 t2);
FStar.Classical.forall_intro #(i:nat{i < length s2}) #(fun i -> index s2 i == index t2 i) (lemma_append_inj_r s1 s2 t... | val lemma_append_inj: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a {length s1 = length t1 \/ length s2 = length t2}
-> Lemma (requires (equal (append s1 s2) (append t1 t2)))
(ensures (equal s1 t1 /\ equal s2 t2))
let lemma_append_inj #_ s1 s2 t1 t2 = | false | null | true | lemma_append_len_disj s1 s2 t1 t2;
FStar.Classical.forall_intro #(i: nat{i < length s1})
#(fun i -> index s1 i == index t1 i)
(lemma_append_inj_l s1 s2 t1 t2);
FStar.Classical.forall_intro #(i: nat{i < length s2})
#(fun i -> index s2 i == index t2 i)
(lemma_append_inj_r s1 s2 t1 t2) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.l_or",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"FStar.Classical.forall_intro",
"Prims.op_LessThan",
"Prims.eq2",
"FStar.Seq.Base.index",
"FStar.Seq.Properties.lemma_append_inj_r",
"Prims.unit",
"FStar.Seq.Properties.lemma_append_in... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_append_inj: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a {length s1 = length t1 \/ length s2 = length t2}
-> Lemma (requires (equal (append s1 s2) (append t1 t2)))
(ensures (equal s1 t1 /\ equal s2 t2)) | [] | FStar.Seq.Properties.lemma_append_inj | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a ->
t1: FStar.Seq.Base.seq a ->
t2:
FStar.Seq.Base.seq a
{ FStar.Seq.Base.length s1 = FStar.Seq.Base.length t1 \/
FStar.Seq.Base.length s2 = FStar.Seq.Base.length t2 }
-> FStar.Pervasives.Lemma
(requires FStar.Seq.Base.... | {
"end_col": 124,
"end_line": 37,
"start_col": 2,
"start_line": 35
} |
FStar.Pervasives.Lemma | val perm_len (#a:eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let perm_len = perm_len' | val perm_len (#a:eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2))
let perm_len = | false | null | true | perm_len' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.perm_len'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val perm_len (#a:eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2)) | [] | FStar.Seq.Properties.perm_len | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma (requires FStar.Seq.Properties.permutation a s1 s2)
(ensures FStar.Seq.Base.length s1 == FStar.Seq.Base.length s2) | {
"end_col": 24,
"end_line": 238,
"start_col": 15,
"start_line": 238
} |
FStar.Pervasives.Lemma | val seq_mem_k: #a:eqtype -> s:seq a -> n:nat{n < Seq.length s} ->
Lemma (requires True)
(ensures (mem (Seq.index s n) s))
[SMTPat (mem (Seq.index s n) s)] | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let seq_mem_k = seq_mem_k' | val seq_mem_k: #a:eqtype -> s:seq a -> n:nat{n < Seq.length s} ->
Lemma (requires True)
(ensures (mem (Seq.index s n) s))
[SMTPat (mem (Seq.index s n) s)]
let seq_mem_k = | false | null | true | seq_mem_k' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.seq_mem_k'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val seq_mem_k: #a:eqtype -> s:seq a -> n:nat{n < Seq.length s} ->
Lemma (requires True)
(ensures (mem (Seq.index s n) s))
[SMTPat (mem (Seq.index s n) s)] | [] | FStar.Seq.Properties.seq_mem_k | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> n: Prims.nat{n < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma (ensures FStar.Seq.Properties.mem (FStar.Seq.Base.index s n) s)
[SMTPat (FStar.Seq.Properties.mem (FStar.Seq.Base.index s n) s)] | {
"end_col": 26,
"end_line": 383,
"start_col": 16,
"start_line": 383
} |
FStar.Pervasives.Lemma | val lemma_seq_list_bij: #a:Type -> s:seq a -> Lemma
(requires (True))
(ensures (seq_of_list (seq_to_list s) == s)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let lemma_seq_list_bij = lemma_seq_list_bij' | val lemma_seq_list_bij: #a:Type -> s:seq a -> Lemma
(requires (True))
(ensures (seq_of_list (seq_to_list s) == s))
let lemma_seq_list_bij = | false | null | true | lemma_seq_list_bij' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.lemma_seq_list_bij'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_list_bij: #a:Type -> s:seq a -> Lemma
(requires (True))
(ensures (seq_of_list (seq_to_list s) == s)) | [] | FStar.Seq.Properties.lemma_seq_list_bij | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures FStar.Seq.Properties.seq_of_list (FStar.Seq.Properties.seq_to_list s) == s) | {
"end_col": 44,
"end_line": 409,
"start_col": 25,
"start_line": 409
} |
Prims.Tot | val contains (#a:Type) (s:seq a) (x:a) : Tot Type0 | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let contains #a s x =
exists (k:nat). k < Seq.length s /\ Seq.index s k == x | val contains (#a:Type) (s:seq a) (x:a) : Tot Type0
let contains #a s x = | false | null | false | exists (k: nat). k < Seq.length s /\ Seq.index s k == x | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"total"
] | [
"FStar.Seq.Base.seq",
"Prims.l_Exists",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.eq2",
"FStar.Seq.Base.index"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val contains (#a:Type) (s:seq a) (x:a) : Tot Type0 | [] | FStar.Seq.Properties.contains | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> x: a -> Type0 | {
"end_col": 56,
"end_line": 438,
"start_col": 2,
"start_line": 438
} |
FStar.Pervasives.Lemma | val lemma_tail_append: #a:Type -> s1:seq a{length s1 > 0} -> s2:seq a -> Lemma
(tail (append s1 s2) == append (tail s1) s2) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_tail_append #_ s1 s2 = cut (equal (tail (append s1 s2)) (append (tail s1) s2)) | val lemma_tail_append: #a:Type -> s1:seq a{length s1 > 0} -> s2:seq a -> Lemma
(tail (append s1 s2) == append (tail s1) s2)
let lemma_tail_append #_ s1 s2 = | false | null | true | cut (equal (tail (append s1 s2)) (append (tail s1) s2)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_GreaterThan",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.tail",
"FStar.Seq.Base.append",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_tail_append: #a:Type -> s1:seq a{length s1 > 0} -> s2:seq a -> Lemma
(tail (append s1 s2) == append (tail s1) s2) | [] | FStar.Seq.Properties.lemma_tail_append | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a {FStar.Seq.Base.length s1 > 0} -> s2: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.tail (FStar.Seq.Base.append s1 s2) ==
FStar.Seq.Base.append (FStar.Seq.Properties.tail s1) s2) | {
"end_col": 88,
"end_line": 41,
"start_col": 33,
"start_line": 41
} |
FStar.Pervasives.Lemma | val mem_index' (#a: eqtype) (x: a) (s: seq a)
: Lemma (requires (mem x s)) (ensures (exists i. index s i == x)) (decreases (length s)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec mem_index' (#a:eqtype) (x:a) (s:seq a)
: Lemma (requires (mem x s))
(ensures (exists i. index s i == x))
(decreases (length s))
= if length s = 0 then ()
else if head s = x then ()
else mem_index' x (tail s) | val mem_index' (#a: eqtype) (x: a) (s: seq a)
: Lemma (requires (mem x s)) (ensures (exists i. index s i == x)) (decreases (length s))
let rec mem_index' (#a: eqtype) (x: a) (s: seq a)
: Lemma (requires (mem x s)) (ensures (exists i. index s i == x)) (decreases (length s)) = | false | null | true | if length s = 0 then () else if head s = x then () else mem_index' x (tail s) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"Prims.bool",
"FStar.Seq.Properties.head",
"FStar.Seq.Properties.mem_index'",
"FStar.Seq.Properties.tail",
"Prims.unit",
"Prims.b2t",
"FStar.Seq.Properties.mem",
"Prims.squash",
"Prims.l_Exists... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val mem_index' (#a: eqtype) (x: a) (s: seq a)
: Lemma (requires (mem x s)) (ensures (exists i. index s i == x)) (decreases (length s)) | [
"recursion"
] | FStar.Seq.Properties.mem_index' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: a -> s: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma (requires FStar.Seq.Properties.mem x s)
(ensures exists (i: Prims.nat{i < FStar.Seq.Base.length s}). FStar.Seq.Base.index s i == x)
(decreases FStar.Seq.Base.length s) | {
"end_col": 32,
"end_line": 58,
"start_col": 6,
"start_line": 56
} |
FStar.Pervasives.Lemma | val find_l_none_no_index (#a:Type) (s:Seq.seq a) (f:(a -> Tot bool)) :
Lemma (requires (None? (find_l f s)))
(ensures (forall (i:nat{i < Seq.length s}). not (f (Seq.index s i))))
(decreases (Seq.length s)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let find_l_none_no_index = find_l_none_no_index' | val find_l_none_no_index (#a:Type) (s:Seq.seq a) (f:(a -> Tot bool)) :
Lemma (requires (None? (find_l f s)))
(ensures (forall (i:nat{i < Seq.length s}). not (f (Seq.index s i))))
(decreases (Seq.length s))
let find_l_none_no_index = | false | null | true | find_l_none_no_index' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Properties.find_l_none_no_index'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_l_none_no_index (#a:Type) (s:Seq.seq a) (f:(a -> Tot bool)) :
Lemma (requires (None? (find_l f s)))
(ensures (forall (i:nat{i < Seq.length s}). not (f (Seq.index s i))))
(decreases (Seq.length s)) | [] | FStar.Seq.Properties.find_l_none_no_index | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma (requires None? (FStar.Seq.Properties.find_l f s))
(ensures
forall (i: Prims.nat{i < FStar.Seq.Base.length s}).
Prims.op_Negation (f (FStar.Seq.Base.index s i)))
(decreases FStar.Seq.Base.length s) | {
"end_col": 48,
"end_line": 493,
"start_col": 27,
"start_line": 493
} |
FStar.Pervasives.Lemma | val lemma_slice_first_in_append: #a:Type -> s1:seq a -> s2:seq a -> i:nat{i <= length s1} -> Lemma
(ensures (equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_slice_first_in_append = lemma_slice_first_in_append' | val lemma_slice_first_in_append: #a:Type -> s1:seq a -> s2:seq a -> i:nat{i <= length s1} -> Lemma
(ensures (equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2)))
let lemma_slice_first_in_append = | false | null | true | lemma_slice_first_in_append' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.lemma_slice_first_in_append'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_slice_first_in_append: #a:Type -> s1:seq a -> s2:seq a -> i:nat{i <= length s1} -> Lemma
(ensures (equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2))) | [] | FStar.Seq.Properties.lemma_slice_first_in_append | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> i: Prims.nat{i <= FStar.Seq.Base.length s1}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Base.equal (FStar.Seq.Base.slice (FStar.Seq.Base.append s1 s2)
i
(FStar.Seq.Base.length (FStar.Seq.Base.append s1 s2)))
(FStar.Seq.... | {
"end_col": 62,
"end_line": 72,
"start_col": 34,
"start_line": 72
} |
FStar.Pervasives.Lemma | val sorted_feq' (#a: Type) (f g: (a -> a -> Tot bool)) (s: seq a {forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s)) (decreases (length s)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec sorted_feq' (#a:Type)
(f g : (a -> a -> Tot bool))
(s:seq a{forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s))
(decreases (length s))
= if length s <= 1 then ()
else sorted_feq' f g (tail s) | val sorted_feq' (#a: Type) (f g: (a -> a -> Tot bool)) (s: seq a {forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s)) (decreases (length s))
let rec sorted_feq' (#a: Type) (f g: (a -> a -> Tot bool)) (s: seq a {forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s)) (... | false | null | true | if length s <= 1 then () else sorted_feq' f g (tail s) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.bool",
"FStar.Seq.Base.seq",
"Prims.l_Forall",
"Prims.eq2",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.sorted_feq'",
"FStar.Seq.Properties.tail",
"Prims.unit",
"Prims.l_True",
"Prims.squash",
"Prims.l_iff",
"Prims.b2t",
"FStar.Seq.Properties.sorted",
... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val sorted_feq' (#a: Type) (f g: (a -> a -> Tot bool)) (s: seq a {forall x y. f x y == g x y})
: Lemma (ensures (sorted f s <==> sorted g s)) (decreases (length s)) | [
"recursion"
] | FStar.Seq.Properties.sorted_feq' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
f: (_: a -> _: a -> Prims.bool) ->
g: (_: a -> _: a -> Prims.bool) ->
s: FStar.Seq.Base.seq a {forall (x: a) (y: a). f x y == g x y}
-> FStar.Pervasives.Lemma
(ensures FStar.Seq.Properties.sorted f s <==> FStar.Seq.Properties.sorted g s)
(decreases FStar.Seq.Base.length s) | {
"end_col": 34,
"end_line": 90,
"start_col": 5,
"start_line": 89
} |
FStar.Pervasives.Lemma | val lemma_append_count_aux: #a:eqtype -> x:a -> lo:seq a -> hi:seq a -> Lemma
(requires True)
(ensures (count x (append lo hi) = (count x lo + count x hi))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_append_count_aux #_ _ lo hi = lemma_append_count lo hi | val lemma_append_count_aux: #a:eqtype -> x:a -> lo:seq a -> hi:seq a -> Lemma
(requires True)
(ensures (count x (append lo hi) = (count x lo + count x hi)))
let lemma_append_count_aux #_ _ lo hi = | false | null | true | lemma_append_count lo hi | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"FStar.Seq.Properties.lemma_append_count",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_append_count_aux: #a:eqtype -> x:a -> lo:seq a -> hi:seq a -> Lemma
(requires True)
(ensures (count x (append lo hi) = (count x lo + count x hi))) | [] | FStar.Seq.Properties.lemma_append_count_aux | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: a -> lo: FStar.Seq.Base.seq a -> hi: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.count x (FStar.Seq.Base.append lo hi) =
FStar.Seq.Properties.count x lo + FStar.Seq.Properties.count x hi) | {
"end_col": 64,
"end_line": 110,
"start_col": 40,
"start_line": 110
} |
FStar.Pervasives.Lemma | val lemma_slice_first_in_append' (#a: Type) (s1 s2: seq a) (i: nat{i <= length s1})
: Lemma
(ensures
(equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2)
)) (decreases (length s1)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec lemma_slice_first_in_append' (#a:Type) (s1:seq a) (s2:seq a)
(i:nat{i <= length s1})
: Lemma
(ensures (equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2)))
(decreases (length s1))
= if i = 0 then ()
else lemma_slice_first_in_append' (tail s1) s2 (i - 1) | val lemma_slice_first_in_append' (#a: Type) (s1 s2: seq a) (i: nat{i <= length s1})
: Lemma
(ensures
(equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2)
)) (decreases (length s1))
let rec lemma_slice_first_in_append' (#a: Type) (s1 s2: seq a) (i: nat{i ... | false | null | true | if i = 0 then () else lemma_slice_first_in_append' (tail s1) s2 (i - 1) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"Prims.op_Equality",
"Prims.int",
"Prims.bool",
"FStar.Seq.Properties.lemma_slice_first_in_append'",
"FStar.Seq.Properties.tail",
"Prims.op_Subtraction",
"Prims.unit",
"Prims.l_True",
"Prim... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_slice_first_in_append' (#a: Type) (s1 s2: seq a) (i: nat{i <= length s1})
: Lemma
(ensures
(equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2)
)) (decreases (length s1)) | [
"recursion"
] | FStar.Seq.Properties.lemma_slice_first_in_append' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> i: Prims.nat{i <= FStar.Seq.Base.length s1}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Base.equal (FStar.Seq.Base.slice (FStar.Seq.Base.append s1 s2)
i
(FStar.Seq.Base.length (FStar.Seq.Base.append s1 s2)))
(... | {
"end_col": 56,
"end_line": 70,
"start_col": 2,
"start_line": 69
} |
FStar.Pervasives.Lemma | val lemma_count_slice: #a:eqtype -> s:seq a -> i:nat{i<=length s} -> Lemma
(requires True)
(ensures (forall x. count x s = count x (slice s 0 i) + count x (slice s i (length s)))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_count_slice #_ s i =
cut (equal s (append (slice s 0 i) (slice s i (length s))));
lemma_append_count (slice s 0 i) (slice s i (length s)) | val lemma_count_slice: #a:eqtype -> s:seq a -> i:nat{i<=length s} -> Lemma
(requires True)
(ensures (forall x. count x s = count x (slice s 0 i) + count x (slice s i (length s))))
let lemma_count_slice #_ s i = | false | null | true | cut (equal s (append (slice s 0 i) (slice s i (length s))));
lemma_append_count (slice s 0 i) (slice s i (length s)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_append_count",
"FStar.Seq.Base.slice",
"Prims.unit",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_count_slice: #a:eqtype -> s:seq a -> i:nat{i<=length s} -> Lemma
(requires True)
(ensures (forall x. count x s = count x (slice s 0 i) + count x (slice s i (length s)))) | [] | FStar.Seq.Properties.lemma_count_slice | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat{i <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.count x s =
FStar.Seq.Properties.count x (FStar.Seq.Base.slice s 0 i) +
FStar.Seq.Properties.count x (FStar.Seq.Base.slice s i (FStar.Seq.Base.... | {
"end_col": 57,
"end_line": 129,
"start_col": 2,
"start_line": 128
} |
FStar.Pervasives.Lemma | val cons_perm: #a:eqtype -> tl:seq a -> s:seq a{length s > 0} ->
Lemma (requires (permutation a tl (tail s)))
(ensures (permutation a (cons (head s) tl) s)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let cons_perm #_ tl s = lemma_tl (head s) tl | val cons_perm: #a:eqtype -> tl:seq a -> s:seq a{length s > 0} ->
Lemma (requires (permutation a tl (tail s)))
(ensures (permutation a (cons (head s) tl) s))
let cons_perm #_ tl s = | false | null | true | lemma_tl (head s) tl | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_GreaterThan",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_tl",
"FStar.Seq.Properties.head",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val cons_perm: #a:eqtype -> tl:seq a -> s:seq a{length s > 0} ->
Lemma (requires (permutation a tl (tail s)))
(ensures (permutation a (cons (head s) tl) s)) | [] | FStar.Seq.Properties.cons_perm | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | tl: FStar.Seq.Base.seq a -> s: FStar.Seq.Base.seq a {FStar.Seq.Base.length s > 0}
-> FStar.Pervasives.Lemma
(requires FStar.Seq.Properties.permutation a tl (FStar.Seq.Properties.tail s))
(ensures
FStar.Seq.Properties.permutation a
(FStar.Seq.Properties.cons (FStar.Seq.Properties.head s) ... | {
"end_col": 44,
"end_line": 240,
"start_col": 24,
"start_line": 240
} |
FStar.Pervasives.Lemma | val lemma_swap_permutes (#a:eqtype) (s:seq a) (i:nat{i<length s}) (j:nat{i <= j && j<length s})
: Lemma (permutation a s (swap s i j)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_swap_permutes #a s i j
= FStar.Classical.forall_intro
#a
#(fun x -> count x s = count x (swap s i j))
(lemma_swap_permutes_aux s i j) | val lemma_swap_permutes (#a:eqtype) (s:seq a) (i:nat{i<length s}) (j:nat{i <= j && j<length s})
: Lemma (permutation a s (swap s i j))
let lemma_swap_permutes #a s i j = | false | null | true | FStar.Classical.forall_intro #a
#(fun x -> count x s = count x (swap s i j))
(lemma_swap_permutes_aux s i j) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"FStar.Classical.forall_intro",
"Prims.op_Equality",
"FStar.Seq.Properties.count",
"FStar.Seq.Properties.swap",
"FStar.Seq.Properties.l... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_swap_permutes (#a:eqtype) (s:seq a) (i:nat{i<length s}) (j:nat{i <= j && j<length s})
: Lemma (permutation a s (swap s i j)) | [] | FStar.Seq.Properties.lemma_swap_permutes | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
i: Prims.nat{i < FStar.Seq.Base.length s} ->
j: Prims.nat{i <= j && j < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures FStar.Seq.Properties.permutation a s (FStar.Seq.Properties.swap s i j)) | {
"end_col": 51,
"end_line": 202,
"start_col": 4,
"start_line": 199
} |
FStar.Pervasives.Lemma | val swap_frame_lo' : #a:Type -> s:seq a -> lo:nat -> i':nat {lo <= i'} -> i:nat{i' <= i} -> j:nat{i <= j && j < length s}
-> Lemma (ensures (slice s lo i' == slice (swap s i j) lo i')) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let swap_frame_lo' #_ s lo i' i j = cut (equal (slice s lo i') (slice (swap s i j) lo i')) | val swap_frame_lo' : #a:Type -> s:seq a -> lo:nat -> i':nat {lo <= i'} -> i:nat{i' <= i} -> j:nat{i <= j && j < length s}
-> Lemma (ensures (slice s lo i' == slice (swap s i j) lo i'))
let swap_frame_lo' #_ s lo i' i j = | false | null | true | cut (equal (slice s lo i') (slice (swap s i j) lo i')) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.slice",
"FStar.Seq.Properties.swap",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val swap_frame_lo' : #a:Type -> s:seq a -> lo:nat -> i':nat {lo <= i'} -> i:nat{i' <= i} -> j:nat{i <= j && j < length s}
-> Lemma (ensures (slice s lo i' == slice (swap s i j) lo i')) | [] | FStar.Seq.Properties.swap_frame_lo' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
lo: Prims.nat ->
i': Prims.nat{lo <= i'} ->
i: Prims.nat{i' <= i} ->
j: Prims.nat{i <= j && j < FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Base.slice s lo i' == FStar.Seq.Base.slice (FStar.Seq.Properties.swap s i j) lo i') | {
"end_col": 90,
"end_line": 262,
"start_col": 36,
"start_line": 262
} |
FStar.Pervasives.Lemma | val splice_refl : #a:Type -> s:seq a -> i:nat -> j:nat{i <= j && j <= length s}
-> Lemma
(ensures (s == splice s i s j)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let splice_refl #_ s i j = cut (equal s (splice s i s j)) | val splice_refl : #a:Type -> s:seq a -> i:nat -> j:nat{i <= j && j <= length s}
-> Lemma
(ensures (s == splice s i s j))
let splice_refl #_ s i j = | false | null | true | cut (equal s (splice s i s j)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.splice",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val splice_refl : #a:Type -> s:seq a -> i:nat -> j:nat{i <= j && j <= length s}
-> Lemma
(ensures (s == splice s i s j)) | [] | FStar.Seq.Properties.splice_refl | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat -> j: Prims.nat{i <= j && j <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma (ensures s == FStar.Seq.Properties.splice s i s j) | {
"end_col": 57,
"end_line": 273,
"start_col": 27,
"start_line": 273
} |
FStar.Pervasives.Lemma | val lemma_swap_permutes_slice : #a:eqtype -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma (ensures (permutation a (slice s start len) (slice (swap s i j) start len))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_swap_permutes_slice #_ s start i j len =
lemma_swap_slice_commute s start i j len;
lemma_swap_permutes (slice s start len) (i - start) (j - start) | val lemma_swap_permutes_slice : #a:eqtype -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma (ensures (permutation a (slice s start len) (slice (swap s i j) start len)))
let lemma_swap_permutes_slice #_ s start i j len = | false | null | true | lemma_swap_slice_commute s start i j len;
lemma_swap_permutes (slice s start len) (i - start) (j - start) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_swap_permutes",
"FStar.Seq.Base.slice",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Seq.Properties.lemma_s... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_swap_permutes_slice : #a:eqtype -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma (ensures (permutation a (slice s start len) (slice (swap s i j) start len))) | [] | FStar.Seq.Properties.lemma_swap_permutes_slice | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
start: Prims.nat ->
i: Prims.nat{start <= i} ->
j: Prims.nat{i <= j} ->
len: Prims.nat{j < len && len <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.permutation a
(FStar.Seq.Base.slice s start len)
(FStar.Se... | {
"end_col": 65,
"end_line": 271,
"start_col": 2,
"start_line": 270
} |
FStar.Pervasives.Lemma | val append_permutations: #a:eqtype -> s1:seq a -> s2:seq a -> s1':seq a -> s2':seq a -> Lemma
(requires permutation a s1 s1' /\ permutation a s2 s2')
(ensures permutation a (append s1 s2) (append s1' s2')) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let append_permutations #a s1 s2 s1' s2' =
(
lemma_append_count s1 s2;
lemma_append_count s1' s2'
) | val append_permutations: #a:eqtype -> s1:seq a -> s2:seq a -> s1':seq a -> s2':seq a -> Lemma
(requires permutation a s1 s1' /\ permutation a s2 s2')
(ensures permutation a (append s1 s2) (append s1' s2'))
let append_permutations #a s1 s2 s1' s2' = | false | null | true | (lemma_append_count s1 s2;
lemma_append_count s1' s2') | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"FStar.Seq.Properties.lemma_append_count",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val append_permutations: #a:eqtype -> s1:seq a -> s2:seq a -> s1':seq a -> s2':seq a -> Lemma
(requires permutation a s1 s1' /\ permutation a s2 s2')
(ensures permutation a (append s1 s2) (append s1' s2')) | [] | FStar.Seq.Properties.append_permutations | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a ->
s1': FStar.Seq.Base.seq a ->
s2': FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(requires
FStar.Seq.Properties.permutation a s1 s1' /\ FStar.Seq.Properties.permutation a s2 s2')
(ensures
FStar.Seq.Properties.permutat... | {
"end_col": 3,
"end_line": 196,
"start_col": 2,
"start_line": 193
} |
FStar.Pervasives.Lemma | val lemma_tail_slice: #a:Type -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma
(requires True)
(ensures (tail (slice s i j) == slice s (i + 1) j))
[SMTPat (tail (slice s i j))] | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_tail_slice #_ s i j =
cut (equal (tail (slice s i j)) (slice s (i + 1) j)) | val lemma_tail_slice: #a:Type -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma
(requires True)
(ensures (tail (slice s i j) == slice s (i + 1) j))
[SMTPat (tail (slice s i j))]
let lemma_tail_slice #_ s i j = | false | null | true | cut (equal (tail (slice s i j)) (slice s (i + 1) j)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.tail",
"FStar.Seq.Base.slice",
"Prims.op_Addition",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_tail_slice: #a:Type -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}
-> Lemma
(requires True)
(ensures (tail (slice s i j) == slice s (i + 1) j))
[SMTPat (tail (slice s i j))] | [] | FStar.Seq.Properties.lemma_tail_slice | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat -> j: Prims.nat{i < j && j <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.tail (FStar.Seq.Base.slice s i j) == FStar.Seq.Base.slice s (i + 1) j)
[SMTPat (FStar.Seq.Properties.tail (FStar.Seq.Base.slice s i j))] | {
"end_col": 54,
"end_line": 284,
"start_col": 2,
"start_line": 284
} |
FStar.Pervasives.Lemma | val find_append_none_s2: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s2)))
(ensures (find_l f (append s1 s2) == find_l f s1)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let find_append_none_s2 = find_append_none_s2' | val find_append_none_s2: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s2)))
(ensures (find_l f (append s1 s2) == find_l f s1))
let find_append_none_s2 = | false | null | true | find_append_none_s2' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Properties.find_append_none_s2'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_append_none_s2: #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s2)))
(ensures (find_l f (append s1 s2) == find_l f s1)) | [] | FStar.Seq.Properties.find_append_none_s2 | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma (requires None? (FStar.Seq.Properties.find_l f s2))
(ensures
FStar.Seq.Properties.find_l f (FStar.Seq.Base.append s1 s2) ==
FStar.Seq.Properties.find_l f s1) | {
"end_col": 46,
"end_line": 359,
"start_col": 26,
"start_line": 359
} |
FStar.Pervasives.Lemma | val lemma_ordering_lo_snoc: #a:eqtype -> f:tot_ord a -> s:seq a -> i:nat -> j:nat{i <= j && j < length s} -> pv:a
-> Lemma (requires ((forall y. mem y (slice s i j) ==> f y pv) /\ f (index s j) pv))
(ensures ((forall y. mem y (slice s i (j + 1)) ==> f y pv))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_ordering_lo_snoc #_ f s i j pv =
cut (equal (slice s i (j + 1)) (append (slice s i j) (create 1 (index s j))));
lemma_mem_append (slice s i j) (create 1 (index s j)) | val lemma_ordering_lo_snoc: #a:eqtype -> f:tot_ord a -> s:seq a -> i:nat -> j:nat{i <= j && j < length s} -> pv:a
-> Lemma (requires ((forall y. mem y (slice s i j) ==> f y pv) /\ f (index s j) pv))
(ensures ((forall y. mem y (slice s i (j + 1)) ==> f y pv)))
let lemma_ordering_lo_snoc #_ f s i j pv = | false | null | true | cut (equal (slice s i (j + 1)) (append (slice s i j) (create 1 (index s j))));
lemma_mem_append (slice s i j) (create 1 (index s j)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Properties.tot_ord",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_mem_append",
"FStar.Seq.Base.slice",
"FStar.Seq.Base.create",
"FStar.Seq.Ba... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_ordering_lo_snoc: #a:eqtype -> f:tot_ord a -> s:seq a -> i:nat -> j:nat{i <= j && j < length s} -> pv:a
-> Lemma (requires ((forall y. mem y (slice s i j) ==> f y pv) /\ f (index s j) pv))
(ensures ((forall y. mem y (slice s i (j + 1)) ==> f y pv))) | [] | FStar.Seq.Properties.lemma_ordering_lo_snoc | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
f: FStar.Seq.Properties.tot_ord a ->
s: FStar.Seq.Base.seq a ->
i: Prims.nat ->
j: Prims.nat{i <= j && j < FStar.Seq.Base.length s} ->
pv: a
-> FStar.Pervasives.Lemma
(requires
(forall (y: a). FStar.Seq.Properties.mem y (FStar.Seq.Base.slice s i j) ==> f y pv) /\
f (FStar.Se... | {
"end_col": 55,
"end_line": 254,
"start_col": 2,
"start_line": 253
} |
FStar.Pervasives.Lemma | val lemma_snoc_inj: #a:Type -> s1:seq a -> s2:seq a -> v1:a -> v2:a
-> Lemma (requires (equal (snoc s1 v1) (snoc s2 v2)))
(ensures (v1 == v2 /\ equal s1 s2)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_snoc_inj #_ s1 s2 v1 v2 =
let t1 = create 1 v1 in
let t2 = create 1 v2 in
lemma_append_inj s1 t1 s2 t2;
assert(head t1 == head t2) | val lemma_snoc_inj: #a:Type -> s1:seq a -> s2:seq a -> v1:a -> v2:a
-> Lemma (requires (equal (snoc s1 v1) (snoc s2 v2)))
(ensures (v1 == v2 /\ equal s1 s2))
let lemma_snoc_inj #_ s1 s2 v1 v2 = | false | null | true | let t1 = create 1 v1 in
let t2 = create 1 v2 in
lemma_append_inj s1 t1 s2 t2;
assert (head t1 == head t2) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims._assert",
"Prims.eq2",
"FStar.Seq.Properties.head",
"Prims.unit",
"FStar.Seq.Properties.lemma_append_inj",
"FStar.Seq.Base.create"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_snoc_inj: #a:Type -> s1:seq a -> s2:seq a -> v1:a -> v2:a
-> Lemma (requires (equal (snoc s1 v1) (snoc s2 v2)))
(ensures (v1 == v2 /\ equal s1 s2)) | [] | FStar.Seq.Properties.lemma_snoc_inj | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> v1: a -> v2: a
-> FStar.Pervasives.Lemma
(requires
FStar.Seq.Base.equal (FStar.Seq.Properties.snoc s1 v1) (FStar.Seq.Properties.snoc s2 v2))
(ensures v1 == v2 /\ FStar.Seq.Base.equal s1 s2) | {
"end_col": 29,
"end_line": 319,
"start_col": 35,
"start_line": 315
} |
FStar.Pervasives.Lemma | val lemma_list_seq_bij' (#a: Type) (l: list a)
: Lemma (requires (True)) (ensures (seq_to_list (seq_of_list l) == l)) (decreases (L.length l)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "F... | false | let rec lemma_list_seq_bij': #a:Type -> l:list a -> Lemma
(requires (True))
(ensures (seq_to_list (seq_of_list l) == l))
(decreases (L.length l))
= fun #_ l ->
lemma_seq_of_list_induction l;
if L.length l = 0 then ()
else (
lemma_list_seq_bij' (L.tl l);
assert(equal (seq_of_list (L.tl l)) (slice ... | val lemma_list_seq_bij' (#a: Type) (l: list a)
: Lemma (requires (True)) (ensures (seq_to_list (seq_of_list l) == l)) (decreases (L.length l))
let rec lemma_list_seq_bij': #a: Type -> l: list a
-> Lemma (requires (True)) (ensures (seq_to_list (seq_of_list l) == l)) (decreases (L.length l)) = | false | null | true | fun #_ l ->
lemma_seq_of_list_induction l;
if L.length l = 0
then ()
else
(lemma_list_seq_bij' (L.tl l);
assert (equal (seq_of_list (L.tl l)) (slice (seq_of_list l) 1 (length (seq_of_list l))))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.list",
"Prims.op_Equality",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.bool",
"Prims._assert",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.seq_of_list",
"FStar.List.Tot.Base.tl",
"FStar.Seq.Base.slice",
"FStar.Seq.Base.length",
"Prims.unit",
"FStar.Seq.Properties.lemma_list_s... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_list_seq_bij' (#a: Type) (l: list a)
: Lemma (requires (True)) (ensures (seq_to_list (seq_of_list l) == l)) (decreases (L.length l)) | [
"recursion"
] | FStar.Seq.Properties.lemma_list_seq_bij' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a
-> FStar.Pervasives.Lemma
(ensures FStar.Seq.Properties.seq_to_list (FStar.Seq.Properties.seq_of_list l) == l)
(decreases FStar.List.Tot.Base.length l) | {
"end_col": 3,
"end_line": 421,
"start_col": 2,
"start_line": 415
} |
FStar.Pervasives.Lemma | val lemma_weaken_frame_right : #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j && j <= k && k <= length s1}
-> Lemma
(requires (s1 == splice s2 i s1 j))
(ensures (s1 == splice s2 i s1 k)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_weaken_frame_right #_ s1 s2 i j k = cut (equal s1 (splice s2 i s1 k)) | val lemma_weaken_frame_right : #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j && j <= k && k <= length s1}
-> Lemma
(requires (s1 == splice s2 i s1 j))
(ensures (s1 == splice s2 i s1 k))
let lemma_weaken_frame_right #_ s1 s2 i j k = | false | null | true | cut (equal s1 (splice s2 i s1 k)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.splice",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_weaken_frame_right : #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat -> k:nat{i <= j && j <= k && k <= length s1}
-> Lemma
(requires (s1 == splice s2 i s1 j))
(ensures (s1 == splice s2 i s1 k)) | [] | FStar.Seq.Properties.lemma_weaken_frame_right | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a {FStar.Seq.Base.length s1 = FStar.Seq.Base.length s2} ->
i: Prims.nat ->
j: Prims.nat ->
k: Prims.nat{i <= j && j <= k && k <= FStar.Seq.Base.length s1}
-> FStar.Pervasives.Lemma (requires s1 == FStar.Seq.Properties.splice s2 i s1 j)
(ens... | {
"end_col": 79,
"end_line": 286,
"start_col": 46,
"start_line": 286
} |
FStar.Pervasives.Lemma | val lemma_tail_snoc: #a:Type -> s:Seq.seq a{Seq.length s > 0} -> x:a
-> Lemma (ensures (tail (snoc s x) == snoc (tail s) x)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_tail_snoc #_ s x = lemma_slice_first_in_append s (Seq.create 1 x) 1 | val lemma_tail_snoc: #a:Type -> s:Seq.seq a{Seq.length s > 0} -> x:a
-> Lemma (ensures (tail (snoc s x) == snoc (tail s) x))
let lemma_tail_snoc #_ s x = | false | null | true | lemma_slice_first_in_append s (Seq.create 1 x) 1 | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_GreaterThan",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_slice_first_in_append",
"FStar.Seq.Base.create",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_tail_snoc: #a:Type -> s:Seq.seq a{Seq.length s > 0} -> x:a
-> Lemma (ensures (tail (snoc s x) == snoc (tail s) x)) | [] | FStar.Seq.Properties.lemma_tail_snoc | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a {FStar.Seq.Base.length s > 0} -> x: a
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.tail (FStar.Seq.Properties.snoc s x) ==
FStar.Seq.Properties.snoc (FStar.Seq.Properties.tail s) x) | {
"end_col": 77,
"end_line": 313,
"start_col": 29,
"start_line": 313
} |
FStar.Pervasives.Lemma | val find_snoc: #a:Type -> s:Seq.seq a -> x:a -> f:(a -> Tot bool)
-> Lemma (ensures (let res = find_l f (snoc s x) in
match res with
| None -> find_l f s == None /\ not (f x)
| Some y -> res == find_l f s \... | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let find_snoc #_ s x f =
if Some? (find_l f s) then find_append_some s (Seq.create 1 x) f
else find_append_none s (Seq.create 1 x) f | val find_snoc: #a:Type -> s:Seq.seq a -> x:a -> f:(a -> Tot bool)
-> Lemma (ensures (let res = find_l f (snoc s x) in
match res with
| None -> find_l f s == None /\ not (f x)
| Some y -> res == find_l f s \... | false | null | true | if Some? (find_l f s)
then find_append_some s (Seq.create 1 x) f
else find_append_none s (Seq.create 1 x) f | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.bool",
"FStar.Pervasives.Native.uu___is_Some",
"FStar.Seq.Properties.find_l",
"FStar.Seq.Properties.find_append_some",
"FStar.Seq.Base.create",
"FStar.Seq.Properties.find_append_none",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_snoc: #a:Type -> s:Seq.seq a -> x:a -> f:(a -> Tot bool)
-> Lemma (ensures (let res = find_l f (snoc s x) in
match res with
| None -> find_l f s == None /\ not (f x)
| Some y -> res == find_l f s \... | [] | FStar.Seq.Properties.find_snoc | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> x: a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma
(ensures
(let res = FStar.Seq.Properties.find_l f (FStar.Seq.Properties.snoc s x) in
(match res with
| FStar.Pervasives.Native.None #_ ->
FStar.Seq.Properties.find_l f s == FStar.Pervasives.Nat... | {
"end_col": 44,
"end_line": 363,
"start_col": 2,
"start_line": 362
} |
FStar.Pervasives.Lemma | val lemma_seq_of_list_induction (#a:Type) (l:list a)
:Lemma (requires True)
(ensures (let s = seq_of_list l in
match l with
| [] -> Seq.equal s empty
| hd::tl -> s == cons hd (seq_of_list tl) /\
head s == hd /\ tail s == (seq_of_list ... | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let lemma_seq_of_list_induction #_ l
= match l with
| [] -> assert_norm (seq_of_list l == Seq.empty)
| hd::tl ->
assert_norm (seq_of_list (hd::tl) == create 1 hd @| seq_of_list tl);
lemma_tl hd (seq_of_list tl) | val lemma_seq_of_list_induction (#a:Type) (l:list a)
:Lemma (requires True)
(ensures (let s = seq_of_list l in
match l with
| [] -> Seq.equal s empty
| hd::tl -> s == cons hd (seq_of_list tl) /\
head s == hd /\ tail s == (seq_of_list ... | false | null | true | match l with
| [] -> assert_norm (seq_of_list l == Seq.empty)
| hd :: tl ->
assert_norm (seq_of_list (hd :: tl) == create 1 hd @| seq_of_list tl);
lemma_tl hd (seq_of_list tl) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.list",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"FStar.Seq.Base.seq",
"Prims.l_or",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.List.Tot.Base.length",
"FStar.Seq.Base.length",
"Prims.int",
"FStar.Seq.Properties.seq_of_list",
"FStar.Seq.Base.empty",
"FStar.Seq.Propertie... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_of_list_induction (#a:Type) (l:list a)
:Lemma (requires True)
(ensures (let s = seq_of_list l in
match l with
| [] -> Seq.equal s empty
| hd::tl -> s == cons hd (seq_of_list tl) /\
head s == hd /\ tail s == (seq_of_list ... | [] | FStar.Seq.Properties.lemma_seq_of_list_induction | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a
-> FStar.Pervasives.Lemma
(ensures
(let s = FStar.Seq.Properties.seq_of_list l in
(match l with
| Prims.Nil #_ -> FStar.Seq.Base.equal s FStar.Seq.Base.empty
| Prims.Cons #_ hd tl ->
s == FStar.Seq.Properties.cons hd (FStar.Seq.Properties.seq_of_list t... | {
"end_col": 34,
"end_line": 392,
"start_col": 4,
"start_line": 388
} |
FStar.Pervasives.Lemma | val lemma_swap_splice : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma
(ensures (swap s i j == splice s start (swap s i j) len)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_swap_splice #_ s start i j len = cut (equal (swap s i j) (splice s start (swap s i j) len)) | val lemma_swap_splice : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma
(ensures (swap s i j == splice s start (swap s i j) len))
let lemma_swap_splice #_ s start i j len = | false | null | true | cut (equal (swap s i j) (splice s start (swap s i j) len)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.swap",
"FStar.Seq.Properties.splice",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_swap_splice : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}
-> Lemma
(ensures (swap s i j == splice s start (swap s i j) len)) | [] | FStar.Seq.Properties.lemma_swap_splice | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
start: Prims.nat ->
i: Prims.nat{start <= i} ->
j: Prims.nat{i <= j} ->
len: Prims.nat{j < len && len <= FStar.Seq.Base.length s}
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.swap s i j ==
FStar.Seq.Properties.splice s start (FStar.Seq.Propert... | {
"end_col": 101,
"end_line": 275,
"start_col": 43,
"start_line": 275
} |
FStar.Pervasives.Lemma | val append_contains_equiv (#a:Type) (s1:seq a) (s2:seq a) (x:a)
: Lemma ((append s1 s2) `contains` x
<==>
(s1 `contains` x \/ s2 `contains` x)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let append_contains_equiv #_ s1 s2 x
= FStar.Classical.move_requires (intro_append_contains_from_disjunction s1 s2) x | val append_contains_equiv (#a:Type) (s1:seq a) (s2:seq a) (x:a)
: Lemma ((append s1 s2) `contains` x
<==>
(s1 `contains` x \/ s2 `contains` x))
let append_contains_equiv #_ s1 s2 x = | false | null | true | FStar.Classical.move_requires (intro_append_contains_from_disjunction s1 s2) x | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"FStar.Classical.move_requires",
"Prims.l_or",
"FStar.Seq.Properties.contains",
"FStar.Seq.Base.append",
"FStar.Seq.Properties.intro_append_contains_from_disjunction",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val append_contains_equiv (#a:Type) (s1:seq a) (s2:seq a) (x:a)
: Lemma ((append s1 s2) `contains` x
<==>
(s1 `contains` x \/ s2 `contains` x)) | [] | FStar.Seq.Properties.append_contains_equiv | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> x: a
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.contains (FStar.Seq.Base.append s1 s2) x <==>
FStar.Seq.Properties.contains s1 x \/ FStar.Seq.Properties.contains s2 x) | {
"end_col": 82,
"end_line": 460,
"start_col": 4,
"start_line": 460
} |
FStar.Pervasives.Lemma | val lemma_seq_frame_lo: #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat{i <= j} -> m:nat{j < m} -> n:nat{m <= n && n <= length s1}
-> Lemma
(requires (s1 == (splice s2 m s1 n)))
(ensures ((slice s1 i j == slice s2 i j) /\ (index s1 j == index s2 j))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_seq_frame_lo #_ s1 s2 i j m n =
cut (equal (slice s1 i j) (slice s2 i j)) | val lemma_seq_frame_lo: #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat{i <= j} -> m:nat{j < m} -> n:nat{m <= n && n <= length s1}
-> Lemma
(requires (s1 == (splice s2 m s1 n)))
(ensures ((slice s1 i j == slice s2 i j) /\ (index s1 j == index s2 j)))
let lemma_seq_frame_lo #_ s1 s2 i j m... | false | null | true | cut (equal (slice s1 i j) (slice s2 i j)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"Prims.op_LessThanOrEqual",
"Prims.op_LessThan",
"Prims.op_AmpAmp",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.slice",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_frame_lo: #a:Type -> s1:seq a -> s2:seq a{length s1 = length s2} -> i:nat -> j:nat{i <= j} -> m:nat{j < m} -> n:nat{m <= n && n <= length s1}
-> Lemma
(requires (s1 == (splice s2 m s1 n)))
(ensures ((slice s1 i j == slice s2 i j) /\ (index s1 j == index s2 j))) | [] | FStar.Seq.Properties.lemma_seq_frame_lo | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a {FStar.Seq.Base.length s1 = FStar.Seq.Base.length s2} ->
i: Prims.nat ->
j: Prims.nat{i <= j} ->
m: Prims.nat{j < m} ->
n: Prims.nat{m <= n && n <= FStar.Seq.Base.length s1}
-> FStar.Pervasives.Lemma (requires s1 == FStar.Seq.Properties.spl... | {
"end_col": 43,
"end_line": 281,
"start_col": 2,
"start_line": 281
} |
FStar.Pervasives.Lemma | val find_append_some' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (Some? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec find_append_some': #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (Some? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1))
= fun #_ s1 s2 f ->
if f (head s1) then ()
else
let _ = cut (equal (tail (append s1 s2)) (append (tail s1) s2... | val find_append_some' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (Some? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1))
let rec find_append_some': #a: Type -> s1: seq a -> s2: seq a -> f: (a -> Tot bool)
-> Lemma (requires (Some? (find_l... | false | null | true | fun #_ s1 s2 f ->
if f (head s1)
then ()
else
let _ = cut (equal (tail (append s1 s2)) (append (tail s1) s2)) in
find_append_some' (tail s1) s2 f | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Base.seq",
"Prims.bool",
"FStar.Seq.Properties.head",
"FStar.Seq.Properties.find_append_some'",
"FStar.Seq.Properties.tail",
"Prims.unit",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_append_some' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (Some? (find_l f s1)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1)) | [
"recursion"
] | FStar.Seq.Properties.find_append_some' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma (requires Some? (FStar.Seq.Properties.find_l f s1))
(ensures
FStar.Seq.Properties.find_l f (FStar.Seq.Base.append s1 s2) ==
FStar.Seq.Properties.find_l f s1)
(decreases FStar.Seq.Base.... | {
"end_col": 36,
"end_line": 331,
"start_col": 2,
"start_line": 327
} |
FStar.Pervasives.Lemma | val lemma_ordering_hi_cons: #a:eqtype -> f:tot_ord a -> s:seq a -> back:nat -> len:nat{back < len && len <= length s} -> pv:a
-> Lemma (requires ((forall y. mem y (slice s (back + 1) len) ==> f pv y) /\ f pv (index s back)))
(ensures ((forall y. mem y (slice s back len) ==> f pv y))) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_ordering_hi_cons #_ f s back len pv =
cut (equal (slice s back len) (append (create 1 (index s back)) (slice s (back + 1) len)));
lemma_mem_append (create 1 (index s back)) (slice s (back + 1) len) | val lemma_ordering_hi_cons: #a:eqtype -> f:tot_ord a -> s:seq a -> back:nat -> len:nat{back < len && len <= length s} -> pv:a
-> Lemma (requires ((forall y. mem y (slice s (back + 1) len) ==> f pv y) /\ f pv (index s back)))
(ensures ((forall y. mem y (slice s back len) ==> f pv y)))
let lemma_ordering_h... | false | null | true | cut (equal (slice s back len) (append (create 1 (index s back)) (slice s (back + 1) len)));
lemma_mem_append (create 1 (index s back)) (slice s (back + 1) len) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"Prims.eqtype",
"FStar.Seq.Properties.tot_ord",
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"Prims.op_LessThanOrEqual",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.lemma_mem_append",
"FStar.Seq.Base.create",
"FStar.Seq.Base.index",
"FStar.Seq.Ba... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_ordering_hi_cons: #a:eqtype -> f:tot_ord a -> s:seq a -> back:nat -> len:nat{back < len && len <= length s} -> pv:a
-> Lemma (requires ((forall y. mem y (slice s (back + 1) len) ==> f pv y) /\ f pv (index s back)))
(ensures ((forall y. mem y (slice s back len) ==> f pv y))) | [] | FStar.Seq.Properties.lemma_ordering_hi_cons | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
f: FStar.Seq.Properties.tot_ord a ->
s: FStar.Seq.Base.seq a ->
back: Prims.nat ->
len: Prims.nat{back < len && len <= FStar.Seq.Base.length s} ->
pv: a
-> FStar.Pervasives.Lemma
(requires
(forall (y: a).
FStar.Seq.Properties.mem y (FStar.Seq.Base.slice s (back + 1) len)... | {
"end_col": 69,
"end_line": 258,
"start_col": 2,
"start_line": 257
} |
FStar.Pervasives.Lemma | val sorted_concat_lemma'
(#a: eqtype)
(f: (a -> a -> Tot bool){total_order a f})
(lo: seq a {sorted f lo})
(pivot: a)
(hi: seq a {sorted f hi})
: Lemma (requires (forall y. (mem y lo ==> f y pivot) /\ (mem y hi ==> f pivot y)))
(ensures (sorted f (append lo (cons pivot hi))))
... | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec sorted_concat_lemma': #a:eqtype
-> f:(a -> a -> Tot bool){total_order a f}
-> lo:seq a{sorted f lo}
-> pivot:a
-> hi:seq a{sorted f hi}
-> Lemma (requires (forall y. (mem y lo ==> f y pivot)
... | val sorted_concat_lemma'
(#a: eqtype)
(f: (a -> a -> Tot bool){total_order a f})
(lo: seq a {sorted f lo})
(pivot: a)
(hi: seq a {sorted f hi})
: Lemma (requires (forall y. (mem y lo ==> f y pivot) /\ (mem y hi ==> f pivot y)))
(ensures (sorted f (append lo (cons pivot hi))))
... | false | null | true | fun #_ f lo pivot hi ->
if length lo = 0
then
(cut (equal (append lo (cons pivot hi)) (cons pivot hi));
cut (equal (tail (cons pivot hi)) hi))
else
(sorted_concat_lemma' f (tail lo) pivot hi;
lemma_append_cons lo (cons pivot hi);
lemma_tl (head lo) (append (tail lo) (cons pivot hi))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.eqtype",
"Prims.bool",
"FStar.Seq.Properties.total_order",
"FStar.Seq.Base.seq",
"Prims.b2t",
"FStar.Seq.Properties.sorted",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.tail",
"FStar.Seq.Properties.cons",
"Pri... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val sorted_concat_lemma'
(#a: eqtype)
(f: (a -> a -> Tot bool){total_order a f})
(lo: seq a {sorted f lo})
(pivot: a)
(hi: seq a {sorted f hi})
: Lemma (requires (forall y. (mem y lo ==> f y pivot) /\ (mem y hi ==> f pivot y)))
(ensures (sorted f (append lo (cons pivot hi))))
... | [
"recursion"
] | FStar.Seq.Properties.sorted_concat_lemma' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
f: (_: a -> _: a -> Prims.bool){FStar.Seq.Properties.total_order a f} ->
lo: FStar.Seq.Base.seq a {FStar.Seq.Properties.sorted f lo} ->
pivot: a ->
hi: FStar.Seq.Base.seq a {FStar.Seq.Properties.sorted f hi}
-> FStar.Pervasives.Lemma
(requires
forall (y: a).
(FStar.Seq.Propert... | {
"end_col": 62,
"end_line": 146,
"start_col": 2,
"start_line": 140
} |
FStar.Pervasives.Lemma | val lemma_swap_permutes_aux_frag_eq: #a:Type -> s:seq a -> i:nat{i<length s} -> j:nat{i <= j && j<length s}
-> i':nat -> j':nat{i' <= j' /\ j'<=length s /\
(j < i' //high slice
\/ j' <= i //low slice
... | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_swap_permutes_aux_frag_eq #a s i j i' j' =
cut (equal (slice s i' j') (slice (swap s i j) i' j'));
cut (equal (slice s i (i + 1)) (slice (swap s i j) j (j + 1)));
cut (equal (slice s j (j + 1)) (slice (swap s i j) i (i + 1))) | val lemma_swap_permutes_aux_frag_eq: #a:Type -> s:seq a -> i:nat{i<length s} -> j:nat{i <= j && j<length s}
-> i':nat -> j':nat{i' <= j' /\ j'<=length s /\
(j < i' //high slice
\/ j' <= i //low slice
... | false | null | true | cut (equal (slice s i' j') (slice (swap s i j) i' j'));
cut (equal (slice s i (i + 1)) (slice (swap s i j) j (j + 1)));
cut (equal (slice s j (j + 1)) (slice (swap s i j) i (i + 1))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"Prims.l_and",
"Prims.l_or",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.slice",
"Prims.op_Addition",
"FStar.Seq.Properties.swap",
"Prims.... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_swap_permutes_aux_frag_eq: #a:Type -> s:seq a -> i:nat{i<length s} -> j:nat{i <= j && j<length s}
-> i':nat -> j':nat{i' <= j' /\ j'<=length s /\
(j < i' //high slice
\/ j' <= i //low slice
... | [] | FStar.Seq.Properties.lemma_swap_permutes_aux_frag_eq | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s: FStar.Seq.Base.seq a ->
i: Prims.nat{i < FStar.Seq.Base.length s} ->
j: Prims.nat{i <= j && j < FStar.Seq.Base.length s} ->
i': Prims.nat ->
j':
Prims.nat
{i' <= j' /\ j' <= FStar.Seq.Base.length s /\ (j < i' \/ j' <= i \/ i < i' /\ j' <= j)}
-> FStar.Pervasives.Lemma
(ensure... | {
"end_col": 65,
"end_line": 161,
"start_col": 2,
"start_line": 159
} |
FStar.Pervasives.Lemma | val lemma_trans_frame : #a:Type -> s1:seq a -> s2:seq a -> s3:seq a{length s1 = length s2 /\ length s2 = length s3} -> i:nat -> j:nat{i <= j && j <= length s1}
-> Lemma
(requires ((s1 == splice s2 i s1 j) /\ s2 == splice s3 i s2 j))
(ensures (s1 == splice s3 i s1 j)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let lemma_trans_frame #_ s1 s2 s3 i j = cut (equal s1 (splice s3 i s1 j)) | val lemma_trans_frame : #a:Type -> s1:seq a -> s2:seq a -> s3:seq a{length s1 = length s2 /\ length s2 = length s3} -> i:nat -> j:nat{i <= j && j <= length s1}
-> Lemma
(requires ((s1 == splice s2 i s1 j) /\ s2 == splice s3 i s2 j))
(ensures (s1 == splice s3 i s1 j))
let lemma_trans_frame #_ s1 s2 s3 i j = | false | null | true | cut (equal s1 (splice s3 i s1 j)) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"Prims.l_and",
"Prims.b2t",
"Prims.op_Equality",
"Prims.nat",
"FStar.Seq.Base.length",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Properties.splice",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_trans_frame : #a:Type -> s1:seq a -> s2:seq a -> s3:seq a{length s1 = length s2 /\ length s2 = length s3} -> i:nat -> j:nat{i <= j && j <= length s1}
-> Lemma
(requires ((s1 == splice s2 i s1 j) /\ s2 == splice s3 i s2 j))
(ensures (s1 == splice s3 i s1 j)) | [] | FStar.Seq.Properties.lemma_trans_frame | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} |
s1: FStar.Seq.Base.seq a ->
s2: FStar.Seq.Base.seq a ->
s3:
FStar.Seq.Base.seq a
{ FStar.Seq.Base.length s1 = FStar.Seq.Base.length s2 /\
FStar.Seq.Base.length s2 = FStar.Seq.Base.length s3 } ->
i: Prims.nat ->
j: Prims.nat{i <= j && j <= FStar.Seq.Base.length s1}
-> FStar... | {
"end_col": 73,
"end_line": 290,
"start_col": 40,
"start_line": 290
} |
Prims.Pure | val split_5 : #a:Type -> s:seq a -> i:nat -> j:nat{i < j && j < length s} -> Pure (seq (seq a))
(requires True)
(ensures (fun x ->
(length x = 5
/\ equal s (append (index x 0) (append (index x 1) (append (index x 2) (append (index x 3) (index x 4)))))
/\ equal (index x 0) (slic... | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FS... | false | let split_5 #a s i j =
let frag_lo = slice s 0 i in
let frag_i = slice s i (i + 1) in
let frag_mid = slice s (i + 1) j in
let frag_j = slice s j (j + 1) in
let frag_hi = slice s (j + 1) (length s) in
upd (upd (upd (upd (create 5 frag_lo) 1 frag_i) 2 frag_mid) 3 frag_j) 4 frag_hi | val split_5 : #a:Type -> s:seq a -> i:nat -> j:nat{i < j && j < length s} -> Pure (seq (seq a))
(requires True)
(ensures (fun x ->
(length x = 5
/\ equal s (append (index x 0) (append (index x 1) (append (index x 2) (append (index x 3) (index x 4)))))
/\ equal (index x 0) (slic... | false | null | false | let frag_lo = slice s 0 i in
let frag_i = slice s i (i + 1) in
let frag_mid = slice s (i + 1) j in
let frag_j = slice s j (j + 1) in
let frag_hi = slice s (j + 1) (length s) in
upd (upd (upd (upd (create 5 frag_lo) 1 frag_i) 2 frag_mid) 3 frag_j) 4 frag_hi | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [] | [
"FStar.Seq.Base.seq",
"Prims.nat",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"FStar.Seq.Base.upd",
"FStar.Seq.Base.create",
"FStar.Seq.Base.slice",
"Prims.op_Addition"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val split_5 : #a:Type -> s:seq a -> i:nat -> j:nat{i < j && j < length s} -> Pure (seq (seq a))
(requires True)
(ensures (fun x ->
(length x = 5
/\ equal s (append (index x 0) (append (index x 1) (append (index x 2) (append (index x 3) (index x 4)))))
/\ equal (index x 0) (slic... | [] | FStar.Seq.Properties.split_5 | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a -> i: Prims.nat -> j: Prims.nat{i < j && j < FStar.Seq.Base.length s}
-> Prims.Pure (FStar.Seq.Base.seq (FStar.Seq.Base.seq a)) | {
"end_col": 81,
"end_line": 156,
"start_col": 22,
"start_line": 150
} |
FStar.Pervasives.Lemma | val lemma_find_l_contains' (#a: Type) (f: (a -> Tot bool)) (l: seq a)
: Lemma (requires True)
(ensures Some? (find_l f l) ==> l `contains` (Some?.v (find_l f l)))
(decreases (Seq.length l)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "F... | false | let rec lemma_find_l_contains' (#a:Type) (f:a -> Tot bool) (l:seq a)
: Lemma (requires True) (ensures Some? (find_l f l) ==> l `contains` (Some?.v (find_l f l)))
(decreases (Seq.length l))
= if length l = 0 then ()
else if f (head l) then ()
else lemma_find_l_contains' f (tail l) | val lemma_find_l_contains' (#a: Type) (f: (a -> Tot bool)) (l: seq a)
: Lemma (requires True)
(ensures Some? (find_l f l) ==> l `contains` (Some?.v (find_l f l)))
(decreases (Seq.length l))
let rec lemma_find_l_contains' (#a: Type) (f: (a -> Tot bool)) (l: seq a)
: Lemma (requires True)
(ensur... | false | null | true | if length l = 0 then () else if f (head l) then () else lemma_find_l_contains' f (tail l) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.bool",
"FStar.Seq.Base.seq",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.Seq.Properties.head",
"FStar.Seq.Properties.lemma_find_l_contains'",
"FStar.Seq.Properties.tail",
"Prims.unit",
"Prims.l_True",
"Prims.squash",
"Prims.l_imp",
"Prims.b2t",
"FStar.Pervasive... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_find_l_contains' (#a: Type) (f: (a -> Tot bool)) (l: seq a)
: Lemma (requires True)
(ensures Some? (find_l f l) ==> l `contains` (Some?.v (find_l f l)))
(decreases (Seq.length l)) | [
"recursion"
] | FStar.Seq.Properties.lemma_find_l_contains' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | f: (_: a -> Prims.bool) -> l: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
Some? (FStar.Seq.Properties.find_l f l) ==>
FStar.Seq.Properties.contains l (Some?.v (FStar.Seq.Properties.find_l f l)))
(decreases FStar.Seq.Base.length l) | {
"end_col": 42,
"end_line": 470,
"start_col": 4,
"start_line": 468
} |
FStar.Pervasives.Lemma | val perm_len' (#a: eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2))
(decreases (length s1)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec perm_len' (#a:eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2))
(decreases (length s1))
= if length s1 = 0 then begin
if length s2 = 0 then ()
else assert (count (index s2 0) s2 > 0)
end
else let s1_hd = head s1 in
... | val perm_len' (#a: eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2))
(decreases (length s1))
let rec perm_len' (#a: eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2))
(decreases (length s1)) ... | false | null | true | if length s1 = 0
then if length s2 = 0 then () else assert (count (index s2 0) s2 > 0)
else
let s1_hd = head s1 in
let s1_tl = tail s1 in
assert (count s1_hd s1 > 0);
assert (count s1_hd s2 > 0);
assert (length s2 > 0);
let s2_hd = head s2 in
let s2_tl = tail s2 in
if s1_hd = s2_hd
then
(assert (p... | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"Prims.eqtype",
"FStar.Seq.Base.seq",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"Prims.bool",
"Prims._assert",
"Prims.b2t",
"Prims.op_GreaterThan",
"FStar.Seq.Properties.count",
"FStar.Seq.Base.index",
"Prims.unit",
"FStar.Seq.Properties.perm_len'",
"FStar.Seq.Properties.p... | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 1,
"initial_ifuel": 1,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val perm_len' (#a: eqtype) (s1 s2: seq a)
: Lemma (requires (permutation a s1 s2))
(ensures (length s1 == length s2))
(decreases (length s1)) | [
"recursion"
] | FStar.Seq.Properties.perm_len' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma (requires FStar.Seq.Properties.permutation a s1 s2)
(ensures FStar.Seq.Base.length s1 == FStar.Seq.Base.length s2)
(decreases FStar.Seq.Base.length s1) | {
"end_col": 33,
"end_line": 235,
"start_col": 4,
"start_line": 214
} |
FStar.Pervasives.Lemma | val contains_cons (#a:Type) (hd:a) (tl:Seq.seq a) (x:a)
: Lemma ((cons hd tl) `contains` x
<==>
(x==hd \/ tl `contains` x)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let contains_cons #_ hd tl x
= append_contains_equiv (Seq.create 1 hd) tl x | val contains_cons (#a:Type) (hd:a) (tl:Seq.seq a) (x:a)
: Lemma ((cons hd tl) `contains` x
<==>
(x==hd \/ tl `contains` x))
let contains_cons #_ hd tl x = | false | null | true | append_contains_equiv (Seq.create 1 hd) tl x | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma"
] | [
"FStar.Seq.Base.seq",
"FStar.Seq.Properties.append_contains_equiv",
"FStar.Seq.Base.create",
"Prims.unit"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val contains_cons (#a:Type) (hd:a) (tl:Seq.seq a) (x:a)
: Lemma ((cons hd tl) `contains` x
<==>
(x==hd \/ tl `contains` x)) | [] | FStar.Seq.Properties.contains_cons | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | hd: a -> tl: FStar.Seq.Base.seq a -> x: a
-> FStar.Pervasives.Lemma
(ensures
FStar.Seq.Properties.contains (FStar.Seq.Properties.cons hd tl) x <==>
x == hd \/ FStar.Seq.Properties.contains tl x) | {
"end_col": 48,
"end_line": 475,
"start_col": 4,
"start_line": 475
} |
FStar.Pervasives.Lemma | val lemma_seq_to_list_permutation (#a:eqtype) (s:seq a)
:Lemma (requires True) (ensures (forall x. count x s == List.Tot.Base.count x (seq_to_list s))) (decreases (length s)) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": ... | false | let lemma_seq_to_list_permutation = lemma_seq_to_list_permutation' | val lemma_seq_to_list_permutation (#a:eqtype) (s:seq a)
:Lemma (requires True) (ensures (forall x. count x s == List.Tot.Base.count x (seq_to_list s))) (decreases (length s))
let lemma_seq_to_list_permutation = | false | null | true | lemma_seq_to_list_permutation' | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Properties.lemma_seq_to_list_permutation'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val lemma_seq_to_list_permutation (#a:eqtype) (s:seq a)
:Lemma (requires True) (ensures (forall x. count x s == List.Tot.Base.count x (seq_to_list s))) (decreases (length s)) | [] | FStar.Seq.Properties.lemma_seq_to_list_permutation | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Seq.Base.seq a
-> FStar.Pervasives.Lemma
(ensures
forall (x: a).
FStar.Seq.Properties.count x s ==
FStar.List.Tot.Base.count x (FStar.Seq.Properties.seq_to_list s))
(decreases FStar.Seq.Base.length s) | {
"end_col": 66,
"end_line": 598,
"start_col": 36,
"start_line": 598
} |
FStar.Pervasives.Lemma | val find_append_none_s2' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (None? (find_l f s2)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1)) | [
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "FStar.Seq.Base",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq.Base",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module"... | false | let rec find_append_none_s2': #a:Type -> s1:seq a -> s2:seq a -> f:(a -> Tot bool) -> Lemma
(requires (None? (find_l f s2)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1))
= fun #_ s1 s2 f ->
if Seq.length s1 = 0 then cut (equal (append s1 s2) s2)
else if f (head s1) then ()
els... | val find_append_none_s2' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (None? (find_l f s2)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1))
let rec find_append_none_s2': #a: Type -> s1: seq a -> s2: seq a -> f: (a -> Tot bool)
-> Lemma (requires (None? (... | false | null | true | fun #_ s1 s2 f ->
if Seq.length s1 = 0
then cut (equal (append s1 s2) s2)
else
if f (head s1)
then ()
else
(find_append_none_s2' (tail s1) s2 f;
cut (equal (tail (append s1 s2)) (append (tail s1) s2))) | {
"checked_file": "FStar.Seq.Properties.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Squash.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.Properties.fst.checked",
"FStar.List.Tot.Base.f... | [
"lemma",
""
] | [
"FStar.Seq.Base.seq",
"Prims.bool",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"Prims.cut",
"FStar.Seq.Base.equal",
"FStar.Seq.Base.append",
"FStar.Seq.Properties.head",
"FStar.Seq.Properties.tail",
"Prims.unit",
"FStar.Seq.Properties.find_append_none_s2'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy and Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by appli... | false | false | FStar.Seq.Properties.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_el... | null | val find_append_none_s2' (#a: Type) (s1 s2: seq a) (f: (a -> Tot bool))
: Lemma (requires (None? (find_l f s2)))
(ensures (find_l f (append s1 s2) == find_l f s1))
(decreases (length s1)) | [
"recursion"
] | FStar.Seq.Properties.find_append_none_s2' | {
"file_name": "ulib/FStar.Seq.Properties.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> f: (_: a -> Prims.bool)
-> FStar.Pervasives.Lemma (requires None? (FStar.Seq.Properties.find_l f s2))
(ensures
FStar.Seq.Properties.find_l f (FStar.Seq.Base.append s1 s2) ==
FStar.Seq.Properties.find_l f s1)
(decreases FStar.Seq.Base.... | {
"end_col": 5,
"end_line": 357,
"start_col": 2,
"start_line": 351
} |
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