task_id stringlengths 21 23 | challenge_id stringlengths 16 16 | proof_assistant stringclasses 1
value | session stringclasses 1
value | repo stringclasses 57
values | revision stringclasses 57
values | file_path stringlengths 13 92 | theory stringlengths 1 48 | variant int64 0 132 | challenge_type stringclasses 1
value | difficulty null | count null | by_centrality bool 1
class | ablation_prob float64 0.5 0.5 | min_depth int64 1 1 | max_depth int64 1 1 | leaves_only bool 1
class | min_size int64 0 0 | max_size stringclasses 1
value | min_centrality int64 0 0 | max_centrality stringclasses 1
value | seed int64 42 42 | n_proofs int64 1 173 | n_ablated int64 1 60 | holes_filled listlengths 1 60 | deleted_lemmas listlengths 1 1 | corollaries listlengths 1 1 | closure_size int64 1 172 | challenge_file_content stringlengths 133 350k | solution_file_content stringlengths 394 351k | solution_diff stringlengths 243 134k | manifest dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ablate_5f4f6362d3fc_3 | ac05193c479fabd6 | lean | lean | github.com/leanprover/LNSym | 5c05220ff970e3bdd7813ad0c9ef3741522c8b92 | Proofs/Experiments/AddLoop/AddLoopTandem.lean | AddLoopTandem | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "correctness",
"depth": 1,
"n_commands": 0,
"n_lines": 177,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Correctness.by_the_method rank\n case v1 =>\n intro s0 h_pre\n simp_all only [Spec.pre, pre, Spec'.assert, asser... | [
{
"name": "program.stepi_0x4005b8_cut",
"text": "theorem program.stepi_0x4005b8_cut (s sn : ArmState)\n (h_program : s.program = program)\n (h_pc : r StateField.PC s = 0x4005b8#64)\n (h_err : r StateField.ERR s = StateError.None)\n (h_step : sn = run 1 s) :\n cut sn = true ∧\n r (StateField.GPR 0#5) s... | [
{
"name": "correctness",
"fan_in": 0,
"n_deps_direct": 13,
"n_deps_transitive": 16,
"n_lines": 181,
"n_chars": 7526,
"n_subproofs": 16,
"n_tactics": 156,
"cyclomatic": 2,
"n_automation": 72,
"n_rewrites": 11,
"n_structural": 10,
"automation_only": false,
"max_... | 16 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Shilpi Goel
Experimental: Use the Correctness module to prove that this program computes the
following via a naive loop that iterates over `x0`:
`x0 := x0 + x1`
... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Shilpi Goel
Experimental: Use the Correctness module to prove that this program computes the
following via a naive loop that iterates over `x0`:
`x0 := x0 + x1`
... | @@ -262,6 +262,40 @@
state_simp_rules, bitvec_rules, minimal_theory]
done
+theorem program.stepi_0x4005b8_cut (s sn : ArmState)
+ (h_program : s.program = program)
+ (h_pc : r StateField.PC s = 0x4005b8#64)
+ (h_err : r StateField.ERR s = StateError.None)
+ (h_step : sn = run 1 s) :
+ cut sn... | {
"repo": "LNSym",
"git_repo": "github.com/leanprover/LNSym",
"revision": "5c05220ff970e3bdd7813ad0c9ef3741522c8b92",
"lean_toolchain": "leanprover/lean4:nightly-2024-10-07",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-del... |
ablate_b53d76645b04_0 | 65f981a29fc64513 | lean | lean | github.com/leanprover/LNSym | 5c05220ff970e3bdd7813ad0c9ef3741522c8b92 | Correctness/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "run_succ'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing s with\n | zero => simp [run]\n | succ n ih => rw [run, ih, run_succ]",
"n_chars": 100,
"n_sub... | [
{
"name": "run_succ",
"text": "theorem run_succ [Sys σ] (s : σ) (n : Nat) : run s (n+1) = run (next s) n :=\n rfl\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 86,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
... | [
{
"name": "run_succ'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Leonardo de Moura, Shilpi Goel
-/
/--
A system with state `σ` is defined by a step relation `next`.
-/
class Sys (σ : Type) where
some : σ -- σ is not the empt... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Leonardo de Moura, Shilpi Goel
-/
/--
A system with state `σ` is defined by a step relation `next`.
-/
class Sys (σ : Type) where
some : σ -- σ is not the empt... | @@ -21,10 +21,13 @@
open Sys
+theorem run_succ [Sys σ] (s : σ) (n : Nat) : run s (n+1) = run (next s) n :=
+ rfl
+
theorem run_succ' [Sys σ] (s : σ) (n : Nat) : run s (n+1) = next (run s n) := by
induction n generalizing s with
| zero => simp [run]
- | succ n ih => sorry
+ | succ n ih => rw [run, ih, run... | {
"repo": "LNSym",
"git_repo": "github.com/leanprover/LNSym",
"revision": "5c05220ff970e3bdd7813ad0c9ef3741522c8b92",
"lean_toolchain": "leanprover/lean4:nightly-2024-10-07",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-del... |
ablate_b3f0408fffe4_0 | 2f5508dd42f416fe | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Utils/MiscLemmas.lean | MiscLemmas | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "modify_perm",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv => enter [1, 1] ; rw [← take_getElem_drop h]\n rw [List.modify_eq_take_cons_drop h]\n -- ...\n repeat rw [List.append_a... | [
{
"name": "take_getElem_drop",
"text": "theorem take_getElem_drop {α : Type u} {l : List α} {n : Nat} (h : n < l.length) :\n l.take n ++ l[n] :: l.drop (n + 1) = l := by\n conv => enter [2] ; rw [← List.take_append_drop n l, ← List.getElem_cons_drop h]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars... | [
{
"name": "modify_perm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 373,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max_nesting": ... | 1 | import Lean
namespace LentilLib
namespace List
theorem modify_perm {α : Type u} {l : List α} {idx : Nat} (h : idx < l.length) (f : α → α) :
List.Perm (l ++ [f (l[idx]'h)]) (l.modify idx f ++ [(l[idx]'h)]) := sorry
def foldrD {β : Type v} (f : β → β → β) (d : β) : List β → β
| [a] => a
| a :: as => f a (foldrD... | import Lean
namespace LentilLib
namespace List
theorem take_getElem_drop {α : Type u} {l : List α} {n : Nat} (h : n < l.length) :
l.take n ++ l[n] :: l.drop (n + 1) = l := by
conv => enter [2] ; rw [← List.take_append_drop n l, ← List.getElem_cons_drop h]
theorem modify_perm {α : Type u} {l : List α} {idx : Nat... | @@ -4,8 +4,18 @@
namespace List
+theorem take_getElem_drop {α : Type u} {l : List α} {n : Nat} (h : n < l.length) :
+ l.take n ++ l[n] :: l.drop (n + 1) = l := by
+ conv => enter [2] ; rw [← List.take_append_drop n l, ← List.getElem_cons_drop h]
+
theorem modify_perm {α : Type u} {l : List α} {idx : Nat} (h : i... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_b3f0408fffe4_1 | 5a34e4de95204fb6 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Utils/MiscLemmas.lean | MiscLemmas | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "find_min'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have ⟨n', hn', ha, hb⟩ := find_min _ h\n exists n' ; apply And.intro ‹_› (And.intro ‹_› _) ; intros ; apply Nat.le_of_not_lt ; i... | [
{
"name": "find_min",
"text": "theorem find_min {p : Nat → Prop} (n : Nat) (h : p n) :\n ∃ n', n' ≤ n ∧ p n' ∧ ∀ m, m < n' → ¬ p m := by\n induction n using Nat.strongRecOn\n rename_i n ih\n by_cases h' : ∃ m, m < n ∧ p m\n · rcases h' with ⟨m, hlt, h'⟩\n have ⟨n', hle, ha, hb⟩ := ih _ hlt h'\n e... | [
{
"name": "find_min'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 289,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nesting": 2
... | 1 | import Lean
namespace LentilLib
namespace List
def foldrD {β : Type v} (f : β → β → β) (d : β) : List β → β
| [a] => a
| a :: as => f a (foldrD f d as)
| [] => d
def containsDuplicateElemHashable {α : Type u} [BEq α] [Hashable α] (l : List α) : Bool :=
-- NOTE: Since `MProd` assumes the same universe level ... | import Lean
namespace LentilLib
namespace List
def foldrD {β : Type v} (f : β → β → β) (d : β) : List β → β
| [a] => a
| a :: as => f a (foldrD f d as)
| [] => d
def containsDuplicateElemHashable {α : Type u} [BEq α] [Hashable α] (l : List α) : Bool :=
-- NOTE: Since `MProd` assumes the same universe level ... | @@ -35,8 +35,20 @@
-- NOTE: usually, the unification is not strong enough to figure out `p`,
-- which would be supplied by the user in practice
+theorem find_min {p : Nat → Prop} (n : Nat) (h : p n) :
+ ∃ n', n' ≤ n ∧ p n' ∧ ∀ m, m < n' → ¬ p m := by
+ induction n using Nat.strongRecOn
+ rename_i n ih
+ by_case... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_50ae626d5cb9_0 | 1f768e0e68196821 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Tactics/Rename.lean | Rename | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "Entails_rename_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Entails ; congr 1 ; rw [renameHyp_pred_same newName idx h]",
"n_chars": 71,
"n_subproofs": 0,
"n_tact... | [
{
"name": "renameHyp_pred_same",
"text": "private theorem renameHyp_pred_same : hyps'.map NamedPred.pred = hyps.map NamedPred.pred := by\n rcases h with rfl | ⟨hidx, rfl⟩\n on_goal 1=> rfl\n dsimp ; rw [List.modify_eq_take_cons_drop hidx]\n conv => enter [2, 2] ; rw [← LentilLib.List.take_getElem_drop h... | [
{
"name": "Entails_rename_aux",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 151,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"max_nest... | 1 | import Lentil.ProofMode.Location
namespace TLA.ProofMode
open Lean Meta Elab Tactic
local macro "renameFun" : term => `((fun ⟨_, pred⟩ => ⟨$(mkIdent `newName), pred⟩))
section
variable {σ : Type u} {hyps hyps' : List (NamedPred σ)} {goal : pred σ} (newName : String)
(idx : Nat) (h : ModifyHypSpecWithIndex hyps h... | import Lentil.ProofMode.Location
namespace TLA.ProofMode
open Lean Meta Elab Tactic
local macro "renameFun" : term => `((fun ⟨_, pred⟩ => ⟨$(mkIdent `newName), pred⟩))
section
variable {σ : Type u} {hyps hyps' : List (NamedPred σ)} {goal : pred σ} (newName : String)
(idx : Nat) (h : ModifyHypSpecWithIndex hyps h... | @@ -12,8 +12,16 @@
(idx : Nat) (h : ModifyHypSpecWithIndex hyps hyps' renameFun idx)
include h
-private theorem Entails_rename_aux : Entails hyps' goal = Entails hyps goal := sorry
+private theorem renameHyp_pred_same : hyps'.map NamedPred.pred = hyps.map NamedPred.pred := by
+ rcases h with rfl | ⟨hidx, rfl⟩
+ ... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_7ca671153fd6_0 | 958315901b13f3e7 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Tactics/Specialize.lean | Specialize | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "Entails_specializeHyp_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h1 h2\n rcases h with rfl | ⟨hidx, rfl⟩\n on_goal 1=> exact h2\n apply Entails_add_new (newHypName := (... | [
{
"name": "Entails_add_new",
"text": "/-- The general thing used in `apply`, `have` and `suffices`. -/\ntheorem Entails_add_new {σ : Type u} {hyps : List (NamedPred σ)} {goal : pred σ}\n (subHyps : List (pred σ)) (hinc : subHyps ⊆ hyps.map NamedPred.pred)\n (newHypName : String) (newHyp : pred σ) :\n ((r... | [
{
"name": "Entails_specializeHyp_aux",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 679,
"n_subproofs": 1,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 8,
"automation_only": false,
... | 1 | import Lentil.ProofMode.Tactics.Rename
namespace TLA.ProofMode
open Lean Meta Elab Tactic LentilLib
/-
Design note: `tla_specialize` should be the shared specialization engine for
proof-mode automation.
The tactic repeatedly looks at the current predicate of one temporal hypothesis
and consumes one user argument ac... | import Lentil.ProofMode.Tactics.Rename
namespace TLA.ProofMode
open Lean Meta Elab Tactic LentilLib
/-
Design note: `tla_specialize` should be the shared specialization engine for
proof-mode automation.
The tactic repeatedly looks at the current predicate of one temporal hypothesis
and consumes one user argument ac... | @@ -24,6 +24,20 @@
name.
-/
+/-- The general thing used in `apply`, `have` and `suffices`. -/
+theorem Entails_add_new {σ : Type u} {hyps : List (NamedPred σ)} {goal : pred σ}
+ (subHyps : List (pred σ)) (hinc : subHyps ⊆ hyps.map NamedPred.pred)
+ (newHypName : String) (newHyp : pred σ) :
+ ((repeatedAnd subHyp... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_cde778aeb5ab_0 | 11a2b08525a7e7a0 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Tactics/Have.lean | Have | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "Entails_duplicate_one_hyp_by_name",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " Entails_duplicate_one_hyp newHypName newHyp (by grind)",
"n_chars": 55,
"n_subproofs": 0,
"n_tactic... | [
{
"name": "Entails_duplicate_one_hyp",
"text": "theorem Entails_duplicate_one_hyp :\n newHyp ∈ hyps.map NamedPred.pred →\n Entails (hyps ++ [⟨newHypName, newHyp⟩]) goal →\n Entails hyps goal := fun h1 => Entails_add_new [newHyp] (by grind) newHypName newHyp (pred_implies_refl _)\n\nomit newHyp in\n",
... | [
{
"name": "Entails_duplicate_one_hyp_by_name",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 307,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,... | 1 | import Lentil.ProofMode.Tactics.Clear
import Lentil.ProofMode.Tactics.Specialize
import Lentil.Expr
namespace TLA.ProofMode
open Lean Meta Elab Tactic LentilLib
open Lean.Parser.Tactic
section
variable {σ : Type u} {hyps : List (NamedPred σ)} {goal : pred σ} (newHypName : String) (newHyp : pred σ)
theorem Entails_... | import Lentil.ProofMode.Tactics.Clear
import Lentil.ProofMode.Tactics.Specialize
import Lentil.Expr
namespace TLA.ProofMode
open Lean Meta Elab Tactic LentilLib
open Lean.Parser.Tactic
section
variable {σ : Type u} {hyps : List (NamedPred σ)} {goal : pred σ} (newHypName : String) (newHyp : pred σ)
theorem Entails_... | @@ -36,10 +36,16 @@
Entails (hyps ++ [⟨newHypName, [tlafml| newHypLHS → newHypRHS ]⟩]) goal →
Entails hyps goal := Entails_have_valid newHypName
+theorem Entails_duplicate_one_hyp :
+ newHyp ∈ hyps.map NamedPred.pred →
+ Entails (hyps ++ [⟨newHypName, newHyp⟩]) goal →
+ Entails hyps goal := fun h1 => Entails... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_0 | 1daf458e31acd1a6 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "always_unroll",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [later_always_comm]\n funext e ; tla_unfold_simp\n constructor\n · intro h ; apply And.intro (h 0) (by aesop)\n · intr... | [
{
"name": "later_always_comm",
"text": "theorem later_always_comm : (◯ □ p) =tla= (□ ◯ p) := by\n funext e ; tla_unfold_simp\n constructor <;> intro h k <;> rw [Nat.add_comm] <;> apply h\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 156,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic"... | [
{
"name": "always_unroll",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 266,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 8,
"automation_only": false,
"max_nesting... | 1 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -79,8 +79,19 @@
variable (p : pred σ)
-- FIXME: These should be automatically generated
-theorem always_unroll : □ p =tla= (p ∧ ◯ □ p) := sorry
+theorem later_always_comm : (◯ □ p) =tla= (□ ◯ p) := by
+ funext e ; tla_unfold_simp
+ constructor <;> intro h k <;> rw [Nat.add_comm] <;> apply h
+theorem always_u... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_1 | b6bd035c1ecb8c7a | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "eventually_idem",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply dual_lemma ; simp [not_eventually, always_idem]",
"n_chars": 59,
"n_subproofs": 0,
"n_tactics": 3,
"c... | [
{
"name": "dual_lemma",
"text": "theorem dual_lemma (p q : pred σ) : ¬ p =tla= ¬ q → (p) =tla= (q) := by\n unfold tla_not ; intro h ; funext e ; have := congrFun h e ; aesop\n\n",
"fan_in": 3,
"n_lines": 4,
"n_chars": 147,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_au... | [
{
"name": "eventually_idem",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 124,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 1 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -62,6 +62,9 @@
variable {σ : Type u}
+theorem dual_lemma (p q : pred σ) : ¬ p =tla= ¬ q → (p) =tla= (q) := by
+ unfold tla_not ; intro h ; funext e ; have := congrFun h e ; aesop
+
theorem pred_eq_iff_iff (p q : pred σ) : (p) =tla= (q) ↔ (p) |-tla- (q) ∧ (q) |-tla- (p) := by
tla_unfold_simp ; constructor
... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_2 | 2caf528bc3bd69c8 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "always_eventually_always",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext e ; ext ; constructor\n on_goal 1=> apply always_weaken\n tla_unfold_simp ; intro kk h k ; exists kk ; in... | [
{
"name": "always_weaken",
"text": "theorem always_weaken : □ p |-tla- (p) := by\n tla_unfold_simp ; intro e h ; apply h 0\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 90,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural... | [
{
"name": "always_eventually_always",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 268,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 8,
"automation_only": false,
"m... | 1 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -79,6 +79,9 @@
variable (p : pred σ)
-- FIXME: These should be automatically generated
+theorem always_weaken : □ p |-tla- (p) := by
+ tla_unfold_simp ; intro e h ; apply h 0
+
theorem not_always : (¬ □ p) =tla= (◇ ¬ p) := by
funext e ; tla_unfold_simp
@@ -100,7 +103,12 @@
theorem eventually_idem : (◇ ◇ ... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_3 | e734bec24999cd15 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "contraposition_for_pred_implies",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n repeat rw [← impl_intro, ← contraposition_for_tla_implies]",
"n_chars": 68,
"n_subproofs": 0,
"... | [
{
"name": "impl_intro",
"text": "theorem impl_intro (p q : pred σ) : |-tla- (p → q) = (p) |-tla- (q) := rfl\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 79,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"autom... | [
{
"name": "contraposition_for_pred_implies",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 152,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 1 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -72,6 +72,8 @@
section structural
+theorem impl_intro (p q : pred σ) : |-tla- (p → q) = (p) |-tla- (q) := rfl
+
end structural
section one
@@ -131,7 +133,8 @@
variable (p q : pred σ)
-theorem contraposition_for_pred_implies : (p) |-tla- (q) = ((¬ q) |-tla- ¬ p) := sorry
+theorem contraposition_for_pred... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_4 | 17de49f70e7d5d1e | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "proof_by_contra",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [contraposition_for_pred_implies] ; tla_unfold_simp",
"n_chars": 60,
"n_subproofs": 0,
"n_tactics": 3,
"... | [
{
"name": "contraposition_for_pred_implies",
"text": "theorem contraposition_for_pred_implies : (p) |-tla- (q) = ((¬ q) |-tla- ¬ p) := by\n repeat rw [← impl_intro, ← contraposition_for_tla_implies]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 152,
"n_subproofs": 0,
"n_tactics": 2,
"... | [
{
"name": "proof_by_contra",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 2 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -133,8 +133,12 @@
variable (p q : pred σ)
-theorem proof_by_contra : (p) |-tla- (q) = (¬ q ∧ p) |-tla- (⊥) := sorry
+theorem contraposition_for_pred_implies : (p) |-tla- (q) = ((¬ q) |-tla- ¬ p) := by
+ repeat rw [← impl_intro, ← contraposition_for_tla_implies]
+theorem proof_by_contra : (p) |-tla- (q) = (¬ ... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_5 | bbff3cfa02db396a | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 2 | [
{
"theorem_name": "always_eventually_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h ; apply always_monotone ; apply eventually_monotone ; assumption",
"n_chars": 78,
"n_subproofs":... | [
{
"name": "eventually_monotone",
"text": "theorem eventually_monotone : (p) |-tla- (q) → ◇ p |-tla- ◇ q := by\n tla_unfold_simp ; aesop\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 101,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
... | [
{
"name": "always_eventually_monotone",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"... | 2 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -134,8 +134,12 @@
theorem always_monotone : (p) |-tla- (q) → □ p |-tla- □ q := by
tla_unfold_simp ; aesop
-theorem always_eventually_monotone : (p) |-tla- (q) → (□ ◇ p) |-tla- (□ ◇ q) := sorry
+theorem eventually_monotone : (p) |-tla- (q) → ◇ p |-tla- ◇ q := by
+ tla_unfold_simp ; aesop
+theorem always_even... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_6 | b4d26e07e55652b5 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 2 | [
{
"theorem_name": "always_eventually_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h ; apply always_monotone ; apply eventually_monotone ; assumption",
"n_chars": 78,
"n_subproofs":... | [
{
"name": "eventually_monotone",
"text": "theorem eventually_monotone : (p) |-tla- (q) → ◇ p |-tla- ◇ q := by\n tla_unfold_simp ; aesop\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 101,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
... | [
{
"name": "eventually_always_monotone",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"... | 2 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -134,8 +134,12 @@
theorem always_monotone : (p) |-tla- (q) → □ p |-tla- □ q := by
tla_unfold_simp ; aesop
-theorem eventually_always_monotone : (p) |-tla- (q) → (◇ □ p) |-tla- (◇ □ q) := sorry
+theorem eventually_monotone : (p) |-tla- (q) → ◇ p |-tla- ◇ q := by
+ tla_unfold_simp ; aesop
+theorem eventually_... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_7 | 1da3bdb7cb2a046c | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "eventually_always_and_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [pred_eq_iff_iff] ; constructor\n on_goal 1=> rw [always_and] ; apply eventually_and_split\n tla_unfold_... | [
{
"name": "eventually_and_split",
"text": "/-- uni-direction, splitting the `∧` inside `◇` -/\n@[tladual]\ntheorem eventually_and_split : (◇ (p ∧ q)) |-tla- (◇ p ∧ ◇ q) := by\n tla_unfold_simp ; aesop\n\n-- NOTE: this __DOES NOT__ apply if we change `∧` into `∀`, unless, e.g. `α` is finite!\n",
"fan_in... | [
{
"name": "eventually_always_and_distrib",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 462,
"n_subproofs": 2,
"n_tactics": 16,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 7,
"automation_only": false,
... | 3 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -157,8 +157,22 @@
theorem eventually_or : (◇ (p ∨ q)) =tla= (◇ p ∨ ◇ q) := by
funext e ; tla_unfold_simp ; aesop
-theorem eventually_always_and_distrib : (◇ □ (p ∧ q)) =tla= (◇ □ p ∧ ◇ □ q) := sorry
+/-- uni-direction, splitting the `∧` inside `◇` -/
+@[tladual]
+theorem eventually_and_split : (◇ (p ∧ q)) |-tl... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_2df6272ff580_8 | 540a0ff7d3ae7a19 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/Basic.lean | Basic | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "always_eventually_or_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply dual_lemma ; simp [tlasimp, not_or, eventually_always_and_distrib]",
"n_chars": 78,
"n_subproofs... | [
{
"name": "eventually_always_and_distrib",
"text": "theorem eventually_always_and_distrib : (◇ □ (p ∧ q)) =tla= (◇ □ p ∧ ◇ □ q) := by\n rw [pred_eq_iff_iff] ; constructor\n on_goal 1=> rw [always_and] ; apply eventually_and_split\n tla_unfold_simp ; intro e n1 h1 n2 h2 ; exists (n1 + n2)\n intro k\n sp... | [
{
"name": "always_eventually_or_distrib",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 5,
"n_chars": 184,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 5 | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | import Lentil.Basic
import Lentil.Tactics.Basic
import Lentil.Gadgets.TheoremLifting
/-! Basic theorems about TLA. -/
open Classical LentilLib
-- lift a bunch of proplemmas first
-- `And`
#tla_lift and_self_iff and_not_self_iff not_and_self_iff and_comm and_assoc
#tla_lift And.left => TLA.and_left
#tla_lift And.rig... | @@ -163,8 +163,19 @@
tla_unfold_simp ; aesop
-- NOTE: this __DOES NOT__ apply if we change `∧` into `∀`, unless, e.g. `α` is finite!
+theorem eventually_always_and_distrib : (◇ □ (p ∧ q)) =tla= (◇ □ p ∧ ◇ □ q) := by
+ rw [pred_eq_iff_iff] ; constructor
+ on_goal 1=> rw [always_and] ; apply eventually_and_split
... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_4bfc8a7883d0_1 | 417b4c5b5feea3d2 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/BigOp.lean | BigOp | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 4 | [
{
"theorem_name": "bigwedge_forall_fintype_list",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [bigwedge_forall_list]\n funext e ; tla_unfold_simp ; apply List.mem_forall_iff_fin_index\n\nomit f in",
... | [
{
"name": "bigwedge_forall_list",
"text": "theorem bigwedge_forall_list : (⋀ x ∈ l, (f x)) =tla= (∀ x, (⌞ x ∈ l ⌟ → (f x))) := by\n induction l with\n | nil => funext e ; tla_unfold_simp\n | cons b l ih =>\n simp [tlasimp, ih]\n funext e ; tla_unfold_simp\n\n",
"fan_in": 4,
"n_lines": 8,
... | [
{
"name": "bigwedge_forall_swap",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 227,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 2 | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | @@ -34,7 +34,18 @@
| nil => simp [true_and]
| cons b l1' ih => simp [and_assoc, ih]
-theorem bigwedge_forall_fintype_list : (⋀ x ∈ l, (f x)) =tla= (∀ x : Fin l.length, (f l[x])) := sorry
+theorem bigwedge_forall_list : (⋀ x ∈ l, (f x)) =tla= (∀ x, (⌞ x ∈ l ⌟ → (f x))) := by
+ induction l with
+ | nil => funex... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_4bfc8a7883d0_2 | 9577f6d8a7a0afff | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/BigOp.lean | BigOp | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 4 | [
{
"theorem_name": "bigwedge_forall_fintype_list",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [bigwedge_forall_list]\n funext e ; tla_unfold_simp ; apply List.mem_forall_iff_fin_index\n\nomit f in",
... | [
{
"name": "bigwedge_forall_list",
"text": "theorem bigwedge_forall_list : (⋀ x ∈ l, (f x)) =tla= (∀ x, (⌞ x ∈ l ⌟ → (f x))) := by\n induction l with\n | nil => funext e ; tla_unfold_simp\n | cons b l ih =>\n simp [tlasimp, ih]\n funext e ; tla_unfold_simp\n\n",
"fan_in": 4,
"n_lines": 8,
... | [
{
"name": "bigwedge_inner_and_split",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 201,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 1 | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | @@ -34,8 +34,16 @@
| nil => simp [true_and]
| cons b l1' ih => simp [and_assoc, ih]
-theorem bigwedge_inner_and_split : (⋀ x ∈ l, (f x) ∧ (g x)) =tla= ((⋀ x ∈ l, (f x)) ∧ (⋀ x ∈ l, (g x))) := sorry
+theorem bigwedge_forall_list : (⋀ x ∈ l, (f x)) =tla= (∀ x, (⌞ x ∈ l ⌟ → (f x))) := by
+ induction l with
+ | n... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_4bfc8a7883d0_3 | 001bb749ab5cfb11 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/BigOp.lean | BigOp | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 4 | [
{
"theorem_name": "bigwedge_forall_fintype_list",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [bigwedge_forall_list]\n funext e ; tla_unfold_simp ; apply List.mem_forall_iff_fin_index\n\nomit f in",
... | [
{
"name": "bigwedge_forall_list",
"text": "theorem bigwedge_forall_list : (⋀ x ∈ l, (f x)) =tla= (∀ x, (⌞ x ∈ l ⌟ → (f x))) := by\n induction l with\n | nil => funext e ; tla_unfold_simp\n | cons b l ih =>\n simp [tlasimp, ih]\n funext e ; tla_unfold_simp\n\n",
"fan_in": 4,
"n_lines": 8,
... | [
{
"name": "always_bigwedge",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 1 | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | @@ -34,8 +34,16 @@
| nil => simp [true_and]
| cons b l1' ih => simp [and_assoc, ih]
-theorem always_bigwedge : (□ ⋀ x ∈ l, (f x)) =tla= (⋀ x ∈ l, □ (f x)) := sorry
+theorem bigwedge_forall_list : (⋀ x ∈ l, (f x)) =tla= (∀ x, (⌞ x ∈ l ⌟ → (f x))) := by
+ induction l with
+ | nil => funext e ; tla_unfold_simp
+... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_4bfc8a7883d0_4 | ac6cdcded2dc0acd | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/BigOp.lean | BigOp | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 3 | [
{
"theorem_name": "bigvee_exists_fintype_list",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [bigvee_exists_list]\n funext e ; tla_unfold_simp ; apply List.mem_exists_iff_fin_index",
"n_chars": 96,... | [
{
"name": "bigvee_exists_list",
"text": "theorem bigvee_exists_list : (⋁ x ∈ l, (f x)) =tla= (∃ x, (⌞ x ∈ l ⌟ ∧ (f x))) := by\n induction l with\n | nil => funext e ; tla_unfold_simp\n | cons b l ih =>\n simp [tlasimp, ih]\n funext e ; tla_unfold_simp\n\n",
"fan_in": 3,
"n_lines": 8,
"n... | [
{
"name": "bigvee_exists_fintype_list",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 197,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"... | 1 | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | @@ -44,8 +44,17 @@
@[tlasimp]
theorem bigvee_list_cons (b : β) : (⋁ x ∈ (b :: l), (f x)) =tla= ((f b) ∨ ⋁ x ∈ l, (f x)) := rfl
-theorem bigvee_exists_fintype_list : (⋁ x ∈ l, (f x)) =tla= (∃ x : Fin l.length, (f l[x])) := sorry
+theorem bigvee_exists_list : (⋁ x ∈ l, (f x)) =tla= (∃ x, (⌞ x ∈ l ⌟ ∧ (f x))) := by
+ ... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_4bfc8a7883d0_5 | 3c3fc72c02b1096a | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/BigOp.lean | BigOp | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 3 | [
{
"theorem_name": "bigvee_exists_fintype_list",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [bigvee_exists_list]\n funext e ; tla_unfold_simp ; apply List.mem_exists_iff_fin_index",
"n_chars": 96,... | [
{
"name": "bigvee_exists_list",
"text": "theorem bigvee_exists_list : (⋁ x ∈ l, (f x)) =tla= (∃ x, (⌞ x ∈ l ⌟ ∧ (f x))) := by\n induction l with\n | nil => funext e ; tla_unfold_simp\n | cons b l ih =>\n simp [tlasimp, ih]\n funext e ; tla_unfold_simp\n\n",
"fan_in": 3,
"n_lines": 8,
"n... | [
{
"name": "bigvee_and_distrib",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 180,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | @@ -44,8 +44,17 @@
@[tlasimp]
theorem bigvee_list_cons (b : β) : (⋁ x ∈ (b :: l), (f x)) =tla= ((f b) ∨ ⋁ x ∈ l, (f x)) := rfl
-theorem bigvee_and_distrib (p : pred α) : (p ∧ ⋁ x ∈ l, (f x)) =tla= (⋁ x ∈ l, p ∧ (f x)) := sorry
+theorem bigvee_exists_list : (⋁ x ∈ l, (f x)) =tla= (∃ x, (⌞ x ∈ l ⌟ ∧ (f x))) := by
+ ... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_4bfc8a7883d0_6 | cb3f3eb3f31fd599 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/BigOp.lean | BigOp | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 3 | [
{
"theorem_name": "bigvee_exists_fintype_list",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [bigvee_exists_list]\n funext e ; tla_unfold_simp ; apply List.mem_exists_iff_fin_index",
"n_chars": 96,... | [
{
"name": "bigvee_exists_list",
"text": "theorem bigvee_exists_list : (⋁ x ∈ l, (f x)) =tla= (∃ x, (⌞ x ∈ l ⌟ ∧ (f x))) := by\n induction l with\n | nil => funext e ; tla_unfold_simp\n | cons b l ih =>\n simp [tlasimp, ih]\n funext e ; tla_unfold_simp\n\n",
"fan_in": 3,
"n_lines": 8,
"n... | [
{
"name": "bigwedge_bigvee_match",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 219,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_n... | 2 | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | import Lentil.Rules.Basic
/-! Theorems about big operators (e.g., `⋀`, `⋁`). -/
open Classical LentilLib
namespace TLA
section bigop
variable {α : Type u} {β : Type v} (f g : β → pred α) (l : List β)
-- FIXME: currently we only have the definition of `fold`, but we do not specify
-- its result, so for each `Folda... | @@ -51,9 +51,17 @@
@[tlasimp]
theorem bigvee_list_cons (b : β) : (⋁ x ∈ (b :: l), (f x)) =tla= ((f b) ∨ ⋁ x ∈ l, (f x)) := rfl
+theorem bigvee_exists_list : (⋁ x ∈ l, (f x)) =tla= (∃ x, (⌞ x ∈ l ⌟ ∧ (f x))) := by
+ induction l with
+ | nil => funext e ; tla_unfold_simp
+ | cons b l ih =>
+ simp [tlasimp, ih]
... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_03029a4af382_0 | 34c7a85cf529f7a9 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Tactics/Monotone.lean | Monotone | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "Entails_monotone_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Entails ; intro hh\n rw [mapHypPreds_preds, h]\n exact hmono _ _ hh",
"n_chars": 80,
"n_subproofs": 0... | [
{
"name": "mapHypPreds_preds",
"text": "theorem mapHypPreds_preds {σ : Type u} (f : pred σ → pred σ) (hyps : List (NamedPred σ)) :\n (mapHypPreds f hyps).map NamedPred.pred = (hyps.map NamedPred.pred).map f := by\n simp [mapHypPreds]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 201,
"n_subp... | [
{
"name": "Entails_monotone_aux",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 346,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_ne... | 1 | import Lentil.ProofMode.Basic
import Lentil.Rules.Basic
namespace TLA.ProofMode
open Lean Meta Elab Tactic
def mapHypPreds {σ : Type u} (f : pred σ → pred σ) (hyps : List (NamedPred σ)) :
List (NamedPred σ) :=
hyps.map fun h => { h with pred := f h.pred }
section
variable {σ : Type u}
theorem repeatedAnd_ma... | import Lentil.ProofMode.Basic
import Lentil.Rules.Basic
namespace TLA.ProofMode
open Lean Meta Elab Tactic
def mapHypPreds {σ : Type u} (f : pred σ → pred σ) (hyps : List (NamedPred σ)) :
List (NamedPred σ) :=
hyps.map fun h => { h with pred := f h.pred }
theorem mapHypPreds_preds {σ : Type u} (f : pred σ → p... | @@ -9,6 +9,10 @@
List (NamedPred σ) :=
hyps.map fun h => { h with pred := f h.pred }
+theorem mapHypPreds_preds {σ : Type u} (f : pred σ → pred σ) (hyps : List (NamedPred σ)) :
+ (mapHypPreds f hyps).map NamedPred.pred = (hyps.map NamedPred.pred).map f := by
+ simp [mapHypPreds]
+
section
variable {σ : ... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_03029a4af382_1 | 001ddaf655b07ebc | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Tactics/Monotone.lean | Monotone | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 3 | [
{
"theorem_name": "Entails_later_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Entails_monotone_aux TLA.later repeatedAnd_map_later TLA.later_monotone",
"n_chars": 74,
"n_subproofs": 0,
... | [
{
"name": "Entails_monotone_aux",
"text": "private theorem Entails_monotone_aux (f : pred σ → pred σ)\n (h : ∀ ps, repeatedAnd (ps.map f) = f (repeatedAnd ps))\n (hmono : ∀ (p q : pred σ), (p) |-tla- (q) → ((f p)) |-tla- ((f q))) :\n Entails hyps goal → Entails (mapHypPreds f hyps) (f goal) := by\n unfo... | [
{
"name": "Entails_later_monotone",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 189,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_... | 3 | import Lentil.ProofMode.Basic
import Lentil.Rules.Basic
namespace TLA.ProofMode
open Lean Meta Elab Tactic
def mapHypPreds {σ : Type u} (f : pred σ → pred σ) (hyps : List (NamedPred σ)) :
List (NamedPred σ) :=
hyps.map fun h => { h with pred := f h.pred }
theorem mapHypPreds_preds {σ : Type u} (f : pred σ → p... | import Lentil.ProofMode.Basic
import Lentil.Rules.Basic
namespace TLA.ProofMode
open Lean Meta Elab Tactic
def mapHypPreds {σ : Type u} (f : pred σ → pred σ) (hyps : List (NamedPred σ)) :
List (NamedPred σ) :=
hyps.map fun h => { h with pred := f h.pred }
theorem mapHypPreds_preds {σ : Type u} (f : pred σ → p... | @@ -32,16 +32,27 @@
variable {hyps : List (NamedPred σ)} {goal : pred σ}
+private theorem Entails_monotone_aux (f : pred σ → pred σ)
+ (h : ∀ ps, repeatedAnd (ps.map f) = f (repeatedAnd ps))
+ (hmono : ∀ (p q : pred σ), (p) |-tla- (q) → ((f p)) |-tla- ((f q))) :
+ Entails hyps goal → Entails (mapHypPreds f hyps... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_0 | 0153cdcb22cc408b | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedAnd_eq_in_iff",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 209,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_ne... | 1 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,8 +14,16 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_1 | 7e958cc4bcd338bf | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedAnd_append",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 197,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 1 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,8 +14,16 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_2 | 3b58a05c67ed2f2f | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedAnd_cons",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 441,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 2 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,8 +14,16 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_3 | 79e2db7ec7ceb0b0 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedAnd_add_duplicate",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 238,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"m... | 1 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,8 +14,17 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_4 | 4ef5f4a6acf50e5c | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedAnd_subset_implies",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 265,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"... | 1 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,8 +14,18 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_5 | a0b1744c7146b9f1 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedImplies_apply",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 322,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_n... | 3 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,8 +14,16 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_6 | 24c79dff50241810 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "Entails_of_valid_repeatedImplies",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 446,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false... | 4 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,8 +14,16 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_7 | 02336972eebc22c2 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedAnd_modifyHyp_reorder",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 653,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 4 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,13 +14,22 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_f... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_980dfc311454_8 | 2f8c475d217b9702 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/ProofMode/Basic.lean | Basic | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "repeatedAnd_eq_in_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [repeatedAnd_eq_bigwedge, bigwedge_forall_list, h]",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 2... | [
{
"name": "repeatedAnd_eq_bigwedge",
"text": "theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :\n ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by\n dsimp [tla_bigwedge, Foldable.fold]\n rw [← List.foldrD_eq_foldr]\n · rfl\n · apply and_true\n\n",
"fan_in": 5,
"n_lines": 8,
"n_chars": 207,... | [
{
"name": "repeatedAnd_map_comm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 425,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_n... | 1 | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | import Lentil.Rules.BigOp
namespace TLA.ProofMode
open TLA LentilLib
structure NamedPred (σ : Type u) where
name : String
pred : pred σ
-- FIXME: How to unify this with `tla_bigwedge`?
def repeatedAnd (ps : List (pred σ)) : pred σ := (List.foldrD tla_and tla_true ps)
def repeatedImplies (ps : List (pred σ)) (q... | @@ -14,6 +14,13 @@
def repeatedImplies (ps : List (pred σ)) (q : pred σ) : pred σ := ps.foldr tla_implies q
-- FIXME: This is not satisfactory ...
+theorem repeatedAnd_eq_bigwedge (ps : List (pred σ)) :
+ ((repeatedAnd ps)) =tla= (⋀ x ∈ ps, x) := by
+ dsimp [tla_bigwedge, Foldable.fold]
+ rw [← List.foldrD_eq_fo... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_b96636c6b378_0 | 9a8c46ee5e3d8a2c | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/WF.lean | WF | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "wf_alt1'",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [wf_alt1] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasimp]",
"n_chars": 80,
"n_subproofs": 0,
"n_tacti... | [
{
"name": "wf_alt1",
"text": "theorem wf_alt1 : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabled a) ∨ □ ◇ ⟨a⟩) := by\n funext e ; unfold weak_fairness ; rw [implies_to_or] ; simp [tlasimp]\n rw [← eventually_or] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasimp]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_cha... | [
{
"name": "wf_alt1'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | import Lentil.Rules.Basic
import Lentil.Gadgets.TheoremDeriving
import Lentil.ProofMode.Tactics
import Lentil.ProofMode.Display
/-! Theorems about weak-fairness. -/
open Classical
namespace TLA
section wf
variable {σ : Type u}
section wf_def
variable {a : action σ}
theorem wf_alt1' : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabl... | import Lentil.Rules.Basic
import Lentil.Gadgets.TheoremDeriving
import Lentil.ProofMode.Tactics
import Lentil.ProofMode.Display
/-! Theorems about weak-fairness. -/
open Classical
namespace TLA
section wf
variable {σ : Type u}
section wf_def
variable {a : action σ}
theorem wf_alt1 : (𝒲ℱ a) =tla= □ ◇ ((¬ Enable... | @@ -17,8 +17,13 @@
variable {a : action σ}
-theorem wf_alt1' : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabled a) ∨ ⟨a⟩) := sorry
+theorem wf_alt1 : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabled a) ∨ □ ◇ ⟨a⟩) := by
+ funext e ; unfold weak_fairness ; rw [implies_to_or] ; simp [tlasimp]
+ rw [← eventually_or] ; (repeat rw [always_eventually_or_di... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_b96636c6b378_1 | 517cb11c2beeba54 | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/WF.lean | WF | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "wf1",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [wf_alt1']\n intro e ⟨hpuntilq, haq, henable, hnext, hwf_alt⟩ k hp\n specialize hwf_alt k ; rcases hwf_alt with ⟨k1, hwf_alt⟩\n ... | [
{
"name": "wf_alt1'",
"text": "theorem wf_alt1' : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabled a) ∨ ⟨a⟩) := by\n rw [wf_alt1] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasimp]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_aut... | [
{
"name": "wf1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 37,
"n_chars": 1513,
"n_subproofs": 1,
"n_tactics": 38,
"cyclomatic": 11,
"n_automation": 6,
"n_rewrites": 3,
"n_structural": 18,
"automation_only": false,
"max_nesting": 8
... | 2 | import Lentil.Rules.Basic
import Lentil.Gadgets.TheoremDeriving
import Lentil.ProofMode.Tactics
import Lentil.ProofMode.Display
/-! Theorems about weak-fairness. -/
open Classical
namespace TLA
section wf
variable {σ : Type u}
section wf_def
variable {a : action σ}
theorem wf_alt1 : (𝒲ℱ a) =tla= □ ◇ ((¬ Enable... | import Lentil.Rules.Basic
import Lentil.Gadgets.TheoremDeriving
import Lentil.ProofMode.Tactics
import Lentil.ProofMode.Display
/-! Theorems about weak-fairness. -/
open Classical
namespace TLA
section wf
variable {σ : Type u}
section wf_def
variable {a : action σ}
theorem wf_alt1 : (𝒲ℱ a) =tla= □ ◇ ((¬ Enable... | @@ -21,6 +21,9 @@
funext e ; unfold weak_fairness ; rw [implies_to_or] ; simp [tlasimp]
rw [← eventually_or] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasimp]
+theorem wf_alt1' : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabled a) ∨ ⟨a⟩) := by
+ rw [wf_alt1] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasim... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_b96636c6b378_2 | 5c2fa716223bc80c | lean | lean | github.com/verse-lab/Lentil | bc3bc567928c4a4d0158496b7c18412f10b3304f | Lentil/Rules/WF.lean | WF | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "wf1",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [wf_alt1']\n intro e ⟨hpuntilq, haq, henable, hnext, hwf_alt⟩ k hp\n specialize hwf_alt k ; rcases hwf_alt with ⟨k1, hwf_alt⟩\n ... | [
{
"name": "wf_alt1'",
"text": "theorem wf_alt1' : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabled a) ∨ ⟨a⟩) := by\n rw [wf_alt1] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasimp]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_aut... | [
{
"name": "wf1_original",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 17,
"n_chars": 594,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting"... | 3 | import Lentil.Rules.Basic
import Lentil.Gadgets.TheoremDeriving
import Lentil.ProofMode.Tactics
import Lentil.ProofMode.Display
/-! Theorems about weak-fairness. -/
open Classical
namespace TLA
section wf
variable {σ : Type u}
section wf_def
variable {a : action σ}
theorem wf_alt1 : (𝒲ℱ a) =tla= □ ◇ ((¬ Enable... | import Lentil.Rules.Basic
import Lentil.Gadgets.TheoremDeriving
import Lentil.ProofMode.Tactics
import Lentil.ProofMode.Display
/-! Theorems about weak-fairness. -/
open Classical
namespace TLA
section wf
variable {σ : Type u}
section wf_def
variable {a : action σ}
theorem wf_alt1 : (𝒲ℱ a) =tla= □ ◇ ((¬ Enable... | @@ -21,6 +21,9 @@
funext e ; unfold weak_fairness ; rw [implies_to_or] ; simp [tlasimp]
rw [← eventually_or] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasimp]
+theorem wf_alt1' : (𝒲ℱ a) =tla= □ ◇ ((¬ Enabled a) ∨ ⟨a⟩) := by
+ rw [wf_alt1] ; (repeat rw [always_eventually_or_distrib]) ; simp [tlasim... | {
"repo": "Lentil",
"git_repo": "github.com/verse-lab/Lentil",
"revision": "bc3bc567928c4a4d0158496b7c18412f10b3304f",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_f2f686fc5735_0 | c87705e17d0d1fc6 | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Sequences.lean | Sequences | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "finseq_unique",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro a b b' sab ib sab' ib'\n apply Or.elim (star_star_inv R_functional sab b' sab') <;> grind",
"n_chars": 105,
... | [
{
"name": "star_star_inv",
"text": "theorem star_star_inv (sab : star R a b) :\n ∀ c, star R a c → star R b c ∨ star R c b := by\n induction sab with grind\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 129,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 2,
"n_automation": 1,
... | [
{
"name": "finseq_unique",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 289,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
/-
Finite sequences of transitions
Zero, one or several transitions: reflexive, transitive closure of `R`.
-/
@[grind] inductive star (R : α → α → Prop) : α ... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
/-
Finite sequences of transitions
Zero, one or several transitions: reflexive, transitive closure of `R`.
-/
@[grind] inductive star (R : α → α → Prop) : α ... | @@ -134,8 +134,14 @@
/-
Uniqueness of finite transition sequences.
-/
+theorem star_star_inv (sab : star R a b) :
+ ∀ c, star R a c → star R b c ∨ star R c b := by
+ induction sab with grind
+
theorem finseq_unique :
- ∀ a b b', star R a b → irred R b → star R a b' → irred R b' → b = b' := sorry
+ ∀ a b b',... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_34918e5121ec_0 | 73d2b2d91e09de2e | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Constprop.lean | Constprop | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "simplif_aexp_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro s a\n induction a\n any_goals grind [mk_PLUS_sound, mk_MINUS_sound]",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "mk_PLUS_sound",
"text": "theorem mk_PLUS_sound :\n ∀ s a1 a2, aeval s (mk_PLUS a1 a2) = aeval s a1 + aeval s a2 := by\n intro s a1 a2\n fun_cases mk_PLUS a1 a2\n <;> (try (simp [aeval]) ; try (simp [mk_PLUS_CONST_sound ]) ; grind)\n next m _ =>\n grind\n\n",
"fan_in": 2,
... | [
{
"name": "simplif_aexp_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 283,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | @@ -92,12 +92,23 @@
intro s a n
fun_cases mk_PLUS_CONST a n <;> grind
+theorem mk_PLUS_sound :
+ ∀ s a1 a2, aeval s (mk_PLUS a1 a2) = aeval s a1 + aeval s a2 := by
+ intro s a1 a2
+ fun_cases mk_PLUS a1 a2
+ <;> (try (simp [aeval]) ; try (simp [mk_PLUS_CONST_sound ]) ; grind)
+ next m _ =>
+ ... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_34918e5121ec_1 | 0a012f19d6c0395e | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Constprop.lean | Constprop | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "fixpoint_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have A : ∀ fuel S,\n fixpoint_rec F fuel S = Top\n \\/ Equal (F (fixpoint_rec F fuel S)) (fixpoin... | [
{
"name": "Equal_Le",
"text": "theorem Equal_Le : ∀ S1 S2, Equal S1 S2 -> Le S1 S2 := by\n intro S1 S2 eq\n unfold Equal at eq\n unfold Le\n intro x n\n have := @Std.HashMap.Equiv.getElem?_eq _ _ _ _ S1 S2 _ _ x eq\n grind\n\n/-\n The abstract, compile-time evaluation of expressions returns `.some v`... | [
{
"name": "fixpoint_sound",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 766,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 4,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | @@ -188,6 +188,20 @@
theorem Le_Join_r : ∀ S1 S2, Le S2 (Join S1 S2) := by intros; grind
+theorem Equal_Le : ∀ S1 S2, Equal S1 S2 -> Le S1 S2 := by
+ intro S1 S2 eq
+ unfold Equal at eq
+ unfold Le
+ intro x n
+ have := @Std.HashMap.Equiv.getElem?_eq _ _ _ _ S1 S2 _ _ x eq
+ grind
+
+/-
+ The abstract, com... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_34918e5121ec_2 | ad8cb0d822259a83 | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Constprop.lean | Constprop | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "Cexec_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 76,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro c\n induction c\n next =>\n intro s1 s2 S1 EXEC\n cases EXEC\n grind\n next x a =>\n intr... | [
{
"name": "Le_Join_l",
"text": "theorem Le_Join_l : ∀ S1 S2, Le S1 (Join S1 S2) := by intros; grind\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 71,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_on... | [
{
"name": "Cexec_sound",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 6,
"n_lines": 86,
"n_chars": 2522,
"n_subproofs": 4,
"n_tactics": 78,
"cyclomatic": 10,
"n_automation": 13,
"n_rewrites": 8,
"n_structural": 30,
"automation_only": false,
"max_nesti... | 6 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | @@ -184,6 +184,8 @@
simp [Join]
grind
+theorem Le_Join_l : ∀ S1 S2, Le S1 (Join S1 S2) := by intros; grind
+
theorem Le_Join_r : ∀ S1 S2, Le S2 (Join S1 S2) := by intros; grind
theorem Equal_Le : ∀ S1 S2, Equal S1 S2 -> Le S1 S2 := by
@@ -421,7 +423,7 @@
· rw [←eq1]
simp
... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_34918e5121ec_3 | b92479954997a771 | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Constprop.lean | Constprop | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "simplif_aexp_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro s a\n induction a\n any_goals grind [mk_PLUS_sound, mk_MINUS_sound]",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "mk_PLUS_sound",
"text": "theorem mk_PLUS_sound :\n ∀ s a1 a2, aeval s (mk_PLUS a1 a2) = aeval s a1 + aeval s a2 := by\n intro s a1 a2\n fun_cases mk_PLUS a1 a2\n <;> (try (simp [aeval]) ; try (simp [mk_PLUS_CONST_sound ]) ; grind)\n next m _ =>\n grind\n\n",
"fan_in": 2,
... | [
{
"name": "cp_aexp_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 221,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | @@ -92,6 +92,14 @@
intro s a n
fun_cases mk_PLUS_CONST a n <;> grind
+theorem mk_PLUS_sound :
+ ∀ s a1 a2, aeval s (mk_PLUS a1 a2) = aeval s a1 + aeval s a2 := by
+ intro s a1 a2
+ fun_cases mk_PLUS a1 a2
+ <;> (try (simp [aeval]) ; try (simp [mk_PLUS_CONST_sound ]) ; grind)
+ next m _ =>
+ ... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_34918e5121ec_4 | 6d2966afbac203cf | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Constprop.lean | Constprop | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "cp_bexp_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro s S AG b\n induction b with grind [mk_EQUAL_sound, mk_LESSEQUAL_sound, mk_AND_sound, mk_NOT_sound]",
"n_chars"... | [
{
"name": "mk_LESSEQUAL_sound",
"text": "theorem mk_LESSEQUAL_sound :\n ∀ s a1 a2, beval s (mk_LESSEQUAL a1 a2) = (aeval s a1 <= aeval s a2) := by\n intro s a1 a2\n fun_cases mk_LESSEQUAL a1 a2 <;> grind\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 170,
"n_subproofs": 0,
"n_tactics... | [
{
"name": "cp_bexp_sound",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 20,
"n_chars": 889,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting"... | 4 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | @@ -137,6 +137,11 @@
intro s a1 a2
fun_cases (mk_EQUAL a1 a2) <;> grind
+theorem mk_LESSEQUAL_sound :
+ ∀ s a1 a2, beval s (mk_LESSEQUAL a1 a2) = (aeval s a1 <= aeval s a2) := by
+ intro s a1 a2
+ fun_cases mk_LESSEQUAL a1 a2 <;> grind
+
theorem mk_NOT_sound :
∀ s b, beval s (mk_NOT b) = ¬ (beval... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_34918e5121ec_5 | 7d115958af5c1d1e | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Constprop.lean | Constprop | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "cp_com_correct_terminating",
"depth": 1,
"n_commands": 0,
"n_lines": 83,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro c s1 s2 S1 EXEC AG\n induction c generalizing s1 s2 S1\n any_goals grind\n case ASSIGN x a =>\... | [
{
"name": "cexec_mk_WHILE_done",
"text": "theorem cexec_mk_WHILE_done : ∀ s1 b c,\n beval s1 b = false ->\n cexec s1 (mk_WHILE b c) s1 := by\n intro s1 b c H\n fun_cases mk_WHILE b c <;> grind\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 4,
... | [
{
"name": "cp_com_correct_terminating",
"fan_in": 0,
"n_deps_direct": 8,
"n_deps_transitive": 15,
"n_lines": 86,
"n_chars": 3225,
"n_subproofs": 2,
"n_tactics": 83,
"cyclomatic": 7,
"n_automation": 17,
"n_rewrites": 9,
"n_structural": 30,
"automation_only": false,... | 14 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import Std.Data.HashMap
/-
8. An optimization: constant propagation
8.1 Simplifying expressions using smart const... | @@ -173,6 +173,12 @@
intro s1 b c1 c2 s2
fun_cases (mk_IFTHENELSE b c1 c2) <;> grind
+theorem cexec_mk_WHILE_done : ∀ s1 b c,
+ beval s1 b = false ->
+ cexec s1 (mk_WHILE b c) s1 := by
+ intro s1 b c H
+ fun_cases mk_WHILE b c <;> grind
+
theorem cexec_mk_WHILE_loop : ∀ b c s1 s2 s3,
beval s1 b ... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_fceac798382a_0 | 618b9b2949d9b851 | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Fixpoints.lean | Fixpoints | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "Le_cardinal",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro S T hyp\n have size_eq : ∀ (S : Store), S.size = S.toList.length := by grind\n rw [size_eq S, size_eq T]\n co... | [
{
"name": "hash_set_incl_size_leq",
"text": "theorem hash_set_incl_size_leq (S1 S2 : Store) : Le S2 S1 → List.Subperm (S1.toList) (S2.toList) := by\n intro LE\n unfold Le at LE\n apply List.subperm_of_subset\n · apply List.Pairwise.imp\n rotate_left\n · exact distinct_keys_toList\n · grind\n ·... | [
{
"name": "Le_cardinal",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 522,
"n_subproofs": 1,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 6,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import LeroyCompilerVerificationCourse.Constprop
import Batteries.Data.List.Perm
universe u
/-
9. More about fixpoi... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import LeroyCompilerVerificationCourse.Constprop
import Batteries.Data.List.Perm
universe u
/-
9. More about fixpoi... | @@ -212,10 +212,40 @@
-/
@[grind] def Increasing (F : Store → Store) := ∀ x y, Le x y → Le (F x) (F y)
+theorem hash_set_incl_size_leq (S1 S2 : Store) : Le S2 S1 → List.Subperm (S1.toList) (S2.toList) := by
+ intro LE
+ unfold Le at LE
+ apply List.subperm_of_subset
+ · apply List.Pairwise.imp
+ rotate_left
... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_fceac798382a_1 | 146e449b629a5b73 | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Fixpoints.lean | Fixpoints | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "fixpoint_join_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have LE : Le (Join Init (F (fixpoint_join Init F))) (fixpoint_join Init F) := by\n apply Eq_Le\n apply fixpoint_... | [
{
"name": "fixpoint_join_eq",
"text": "theorem fixpoint_join_eq : Eq' (Join Init (F (fixpoint_join Init F) )) (fixpoint_join Init F) := by\n generalize heq1 : fixpoint_join Init F = t\n apply Eq'_sym\n simp [fixpoint_join] at *\n have := (@iterate_correct Store _ (fun x => Join Init (F x)) _ ?_ ?_ ?_ ?_... | [
{
"name": "fixpoint_join_sound",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 15,
"n_chars": 414,
"n_subproofs": 1,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import LeroyCompilerVerificationCourse.Constprop
import Batteries.Data.List.Perm
universe u
/-
9. More about fixpoi... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import LeroyCompilerVerificationCourse.Constprop
import Batteries.Data.List.Perm
universe u
/-
9. More about fixpoi... | @@ -307,8 +307,24 @@
specialize hyp x
grind
+theorem fixpoint_join_eq : Eq' (Join Init (F (fixpoint_join Init F) )) (fixpoint_join Init F) := by
+ generalize heq1 : fixpoint_join Init F = t
+ apply Eq'_sym
+ simp [fixpoint_join] at *
+ have := (@iterate_correct Store _ (fun x => Join Init (F x)) _ ?_ ?_ ?_ ... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_fceac798382a_2 | e4b0f6e478254e4e | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Fixpoints.lean | Fixpoints | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "fixpoint_join_increasing",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hyp\n apply @fixpoint_join_smallest S1 F (by grind [wrapper]) (fixpoint_join' S2 F F_mon)\n generalize he... | [
{
"name": "fixpoint_join_smallest",
"text": "theorem fixpoint_join_smallest :\n ∀ S, Le (Join Init (F S)) S -> Le (fixpoint_join Init F) S := by\n intro S LE\n unfold fixpoint_join\n have := (@iterate_correct Store _ (fun x => Join Init (F x)) _ (fixpoint_join Init F) Init (?_) ?_ ?_).2 S LE\n ... | [
{
"name": "fixpoint_join_increasing",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 6,
"n_lines": 21,
"n_chars": 717,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 8,
"automation_only": false,
"... | 2 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import LeroyCompilerVerificationCourse.Constprop
import Batteries.Data.List.Perm
universe u
/-
9. More about fixpoi... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
import LeroyCompilerVerificationCourse.Constprop
import Batteries.Data.List.Perm
universe u
/-
9. More about fixpoi... | @@ -321,6 +321,27 @@
grind
· rw [heq1]
+theorem fixpoint_join_smallest :
+ ∀ S, Le (Join Init (F S)) S -> Le (fixpoint_join Init F) S := by
+ intro S LE
+ unfold fixpoint_join
+ have := (@iterate_correct Store _ (fun x => Join Init (F x)) _ (fixpoint_join Init F) Init (?_) ?_ ?_).2 S LE
+ exact t... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_05a739812507_2 | d8f33a913429b46e | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Compil.lean | Compil | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "simulation_step",
"depth": 1,
"n_commands": 0,
"n_lines": 162,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro C impconf1 impconf2 matchconf1 STEP MATCH\n cases MATCH\n case match_config_intro c k st pc h₁ h₂ =>\n ... | [
{
"name": "compile_cont_Kseq_inv",
"text": "theorem compile_cont_Kseq_inv (C : List instr) (c : com) (k :cont) (pc : Int) (s : store) (H : compile_cont C (.Kseq c k) pc) :\n ∃ pc',\n star (transition C) (pc, [], s) (pc', [], s)\n ∧ code_at C pc' (compile_com c)\n ∧ compile_cont C k (pc' + codelen (compi... | [
{
"name": "simulation_step",
"fan_in": 2,
"n_deps_direct": 8,
"n_deps_transitive": 10,
"n_lines": 179,
"n_chars": 5656,
"n_subproofs": 3,
"n_tactics": 164,
"cyclomatic": 27,
"n_automation": 49,
"n_rewrites": 6,
"n_structural": 75,
"automation_only": false,
"ma... | 5 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | @@ -548,6 +548,16 @@
/-
A few technical lemmas to help with the simulation proof.
-/
+theorem compile_cont_Kseq_inv (C : List instr) (c : com) (k :cont) (pc : Int) (s : store) (H : compile_cont C (.Kseq c k) pc) :
+ ∃ pc',
+ star (transition C) (pc, [], s) (pc', [], s)
+ ∧ code_at C pc' (compile_com c)
+ ∧ com... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_05a739812507_3 | 97723cad4d4153d4 | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Compil.lean | Compil | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "simulation_step",
"depth": 1,
"n_commands": 0,
"n_lines": 162,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro C impconf1 impconf2 matchconf1 STEP MATCH\n cases MATCH\n case match_config_intro c k st pc h₁ h₂ =>\n ... | [
{
"name": "compile_cont_Kwhile_inv",
"text": "theorem compile_cont_Kwhile_inv (C : List instr) (b : bexp) (c : com) (k : cont) (pc : Int) (s : store) (H : compile_cont C (.Kwhile b c k) pc) :\n ∃ pc',\n plus (transition C) (pc, [], s) (pc', [], s)\n ∧ code_at C pc' (compile_com (.WHILE b c))\n ∧ compile... | [
{
"name": "simulation_steps",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 32,
"n_chars": 1049,
"n_subproofs": 2,
"n_tactics": 25,
"cyclomatic": 6,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 18,
"automation_only": false,
"max_n... | 6 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | @@ -558,6 +558,35 @@
rw [h₁, h₂] at H
induction H generalizing pc k with grind
+theorem compile_cont_Kwhile_inv (C : List instr) (b : bexp) (c : com) (k : cont) (pc : Int) (s : store) (H : compile_cont C (.Kwhile b c k) pc) :
+ ∃ pc',
+ plus (transition C) (pc, [], s) (pc', [], s)
+ ∧ code_at C pc' (comp... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_05a739812507_4 | 20e66acb4eabbd2a | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Compil.lean | Compil | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "simulation_steps",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro C impconf1 impconf2 STAR machconf1 MATCH\n induction STAR generalizing machconf1\n case star_refl x =... | [
{
"name": "simulation_step",
"text": "theorem simulation_step :\n ∀ C impconf1 impconf2 machconf1,\n step impconf1 impconf2 ->\n match_config C impconf1 machconf1 ->\n ∃ machconf2,\n (plus (transition C) machconf1 machconf2\n \\/ (star (transition C) machconf1 machconf2\n /\\ (measu... | [
{
"name": "compile_program_correct_terminating_2",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 14,
"n_lines": 24,
"n_chars": 905,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 8,
"automation_only"... | 9 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | @@ -607,12 +607,214 @@
/-
At last, we can state and prove the simulation diagram.
-/
+theorem simulation_step :
+ ∀ C impconf1 impconf2 machconf1,
+ step impconf1 impconf2 ->
+ match_config C impconf1 machconf1 ->
+ ∃ machconf2,
+ (plus (transition C) machconf1 machconf2
+ \/ (star (transition C) ma... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_05a739812507_5 | 635685d32743cd4a | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Compil.lean | Compil | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "simulation_step",
"depth": 1,
"n_commands": 0,
"n_lines": 162,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro C impconf1 impconf2 matchconf1 STEP MATCH\n cases MATCH\n case match_config_intro c k st pc h₁ h₂ =>\n ... | [
{
"name": "compile_cont_Kwhile_inv",
"text": "theorem compile_cont_Kwhile_inv (C : List instr) (b : bexp) (c : com) (k : cont) (pc : Int) (s : store) (H : compile_cont C (.Kwhile b c k) pc) :\n ∃ pc',\n plus (transition C) (pc, [], s) (pc', [], s)\n ∧ code_at C pc' (compile_com (.WHILE b c))\n ∧ compile... | [
{
"name": "simulation_infseq_inv",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 34,
"n_chars": 1051,
"n_subproofs": 1,
"n_tactics": 25,
"cyclomatic": 8,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 18,
"automation_only": false,
"... | 6 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | @@ -558,6 +558,35 @@
rw [h₁, h₂] at H
induction H generalizing pc k with grind
+theorem compile_cont_Kwhile_inv (C : List instr) (b : bexp) (c : com) (k : cont) (pc : Int) (s : store) (H : compile_cont C (.Kwhile b c k) pc) :
+ ∃ pc',
+ plus (transition C) (pc, [], s) (pc', [], s)
+ ∧ code_at C pc' (comp... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_05a739812507_6 | 14d241020f00a74e | lean | lean | github.com/leanprover/LeroyCompilerVerificationCourse | a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01 | LeroyCompilerVerificationCourse/Compil.lean | Compil | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "simulation_steps",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro C impconf1 impconf2 STAR machconf1 MATCH\n induction STAR generalizing machconf1\n case star_refl x =... | [
{
"name": "simulation_step",
"text": "theorem simulation_step :\n ∀ C impconf1 impconf2 machconf1,\n step impconf1 impconf2 ->\n match_config C impconf1 machconf1 ->\n ∃ machconf2,\n (plus (transition C) machconf1 machconf2\n \\/ (star (transition C) machconf1 machconf2\n /\\ (measu... | [
{
"name": "compile_program_correct_diverging",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 13,
"n_lines": 21,
"n_chars": 785,
"n_subproofs": 2,
"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 10,
"automation_only": f... | 8 | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under LGPL 2.1 license as described in the file LICENSE.md.
Authors: Wojciech Różowski
-/
import LeroyCompilerVerificationCourse.Imp
/-
2. The target language: a stack machine
Our compiler will translate IMP to the language of a simple stack
ma... | @@ -596,6 +596,184 @@
/-
At last, we can state and prove the simulation diagram.
-/
+theorem simulation_step :
+ ∀ C impconf1 impconf2 machconf1,
+ step impconf1 impconf2 ->
+ match_config C impconf1 machconf1 ->
+ ∃ machconf2,
+ (plus (transition C) machconf1 machconf2
+ \/ (star (transition C) mac... | {
"repo": "LeroyCompilerVerificationCourse",
"git_repo": "github.com/leanprover/LeroyCompilerVerificationCourse",
"revision": "a2730e7f9228b9d7ecf4510f1f8652f2cae7ba01",
"lean_toolchain": "leanprover/lean4:v4.23.0-rc2",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all... |
ablate_874e01a1e9ca_0 | 39cefca418f5c0c7 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/AdaptiveComposition.lean | AdaptiveComposition | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "privComposeAdaptive_renyi_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 84,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Open the definition of Renyi divergence\n unfold RenyiDivergence\n rw [<- (GaloisConnection.l_iSup ga... | [
{
"name": "sup_lemma",
"text": "lemma sup_lemma {U : Type} {s : EReal} (HS0 : 0 < s) (HS1 : s < ⊤) (f : U -> EReal) :\n eexp (s * ⨆ (u : U), f u) = ⨆ (u : U), eexp (s * f u) := by\n rw [@GaloisConnection.l_iSup _ _ _ _ _ _ _ (galois_connection_smul_l HS0 HS1) f]\n apply GaloisConnection.l_iSup galois_... | [
{
"name": "privComposeAdaptive_renyi_bound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 93,
"n_chars": 2885,
"n_subproofs": 5,
"n_tactics": 67,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 30,
"n_structural": 20,
"automation_only": fa... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Adaptive Composition
This ... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Adaptive Composition
This ... | @@ -20,6 +20,11 @@
variable { T : Type }
+lemma sup_lemma {U : Type} {s : EReal} (HS0 : 0 < s) (HS1 : s < ⊤) (f : U -> EReal) :
+ eexp (s * ⨆ (u : U), f u) = ⨆ (u : U), eexp (s * f u) := by
+ rw [@GaloisConnection.l_iSup _ _ _ _ _ _ _ (galois_connection_smul_l HS0 HS1) f]
+ apply GaloisConnection.l_iSup galo... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_874e01a1e9ca_1 | 447ce3183602d80d | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/AdaptiveComposition.lean | AdaptiveComposition | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "privComposeAdaptive_renyi_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 84,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Open the definition of Renyi divergence\n unfold RenyiDivergence\n rw [<- (GaloisConnection.l_iSup ga... | [
{
"name": "sup_lemma",
"text": "lemma sup_lemma {U : Type} {s : EReal} (HS0 : 0 < s) (HS1 : s < ⊤) (f : U -> EReal) :\n eexp (s * ⨆ (u : U), f u) = ⨆ (u : U), eexp (s * f u) := by\n rw [@GaloisConnection.l_iSup _ _ _ _ _ _ _ (galois_connection_smul_l HS0 HS1) f]\n apply GaloisConnection.l_iSup galois_... | [
{
"name": "privComposeAdaptive_zCDPBound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 29,
"n_chars": 1312,
"n_subproofs": 1,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 7,
"automation_only": false,... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Adaptive Composition
This ... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Adaptive Composition
This ... | @@ -20,6 +20,11 @@
variable { T : Type }
+lemma sup_lemma {U : Type} {s : EReal} (HS0 : 0 < s) (HS1 : s < ⊤) (f : U -> EReal) :
+ eexp (s * ⨆ (u : U), f u) = ⨆ (u : U), eexp (s * f u) := by
+ rw [@GaloisConnection.l_iSup _ _ _ _ _ _ _ (galois_connection_smul_l HS0 HS1) f]
+ apply GaloisConnection.l_iSup galo... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_874e01a1e9ca_2 | 786b1720afd99364 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/AdaptiveComposition.lean | AdaptiveComposition | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "privComposeAdaptive_renyi_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 84,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Open the definition of Renyi divergence\n unfold RenyiDivergence\n rw [<- (GaloisConnection.l_iSup ga... | [
{
"name": "sup_lemma",
"text": "lemma sup_lemma {U : Type} {s : EReal} (HS0 : 0 < s) (HS1 : s < ⊤) (f : U -> EReal) :\n eexp (s * ⨆ (u : U), f u) = ⨆ (u : U), eexp (s * f u) := by\n rw [@GaloisConnection.l_iSup _ _ _ _ _ _ _ (galois_connection_smul_l HS0 HS1) f]\n apply GaloisConnection.l_iSup galois_... | [
{
"name": "privComposeAdaptive_zCDP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 412,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"m... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Adaptive Composition
This ... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Adaptive Composition
This ... | @@ -20,6 +20,11 @@
variable { T : Type }
+lemma sup_lemma {U : Type} {s : EReal} (HS0 : 0 < s) (HS1 : s < ⊤) (f : U -> EReal) :
+ eexp (s * ⨆ (u : U), f u) = ⨆ (u : U), eexp (s * f u) := by
+ rw [@GaloisConnection.l_iSup _ _ _ _ _ _ _ (galois_connection_smul_l HS0 HS1) f]
+ apply GaloisConnection.l_iSup galo... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_0 | 5595a48d70c2f9d5 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "ApproximateDP_HαSpecial_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 61,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Eq.le\n rw [Dα]\n conv =>\n enter [1, 1, 1]\n simp\n rw [add_sub_assoc]\n rw [← EReal.co... | [
{
"name": "HαSpecial_algebraic",
"text": "/--\nAlgebraic identity used in the proof that zCDP implies approximate DP.\n\nGiven `S = (2 * D)^(1/2)`, `α - 1 = S / ε`, and `ε' = ε²/2 + ε * S`,\nthis shows `(α - 1) * (ε² * α / 2) = (α - 1) * ε' + log(δ)`.\n-/\nlemma HαSpecial_algebraic {ε S D : ℝ} (Hε : ε ≠ 0) ... | [
{
"name": "ApproximateDP_HαSpecial_bound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 68,
"n_chars": 2206,
"n_subproofs": 2,
"n_tactics": 63,
"cyclomatic": 2,
"n_automation": 14,
"n_rewrites": 32,
"n_structural": 17,
"automation_only": fal... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -57,12 +57,85 @@
-/
def zCDP (q : List T → PMF U) (ε : NNReal) : Prop := ACNeighbour q ∧ zCDPBound q ε
+/--
+Algebraic identity used in the proof that zCDP implies approximate DP.
+
+Given `S = (2 * D)^(1/2)`, `α - 1 = S / ε`, and `ε' = ε²/2 + ε * S`,
+this shows `(α - 1) * (ε² * α / 2) = (α - 1) * ε' + log(δ)`.... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_1 | c7d4a6424237ed6e | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "ApproximateDP_renyi_tsum_le",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs =>\n rw [show (fun x => m₁ x * (m₁ x / m₂ x) ^ (α.toEReal - 1).toReal) =\n (fun x => m₁ ... | [
{
"name": "ApproximateDP_renyi_pointwise_eq",
"text": "lemma ApproximateDP_renyi_pointwise_eq {V : Type*} (p q : PMF V)\n (Hpq : AbsCts p q) (Hqp : AbsCts q p) (α : ℝ) (Hα : 1 < α) (u : V) :\n p u * (p u / q u) ^ (α.toEReal - 1).toReal =\n (p u) ^ α * (q u) ^ (1 - α) := by\n cases (Classical.em (q... | [
{
"name": "ApproximateDP_renyi_tsum_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 54,
"n_chars": 1963,
"n_subproofs": 0,
"n_tactics": 49,
"cyclomatic": 4,
"n_automation": 9,
"n_rewrites": 17,
"n_structural": 20,
"automation_only": false,... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -57,12 +57,97 @@
-/
def zCDP (q : List T → PMF U) (ε : NNReal) : Prop := ACNeighbour q ∧ zCDPBound q ε
+lemma ApproximateDP_renyi_pointwise_eq {V : Type*} (p q : PMF V)
+ (Hpq : AbsCts p q) (Hqp : AbsCts q p) (α : ℝ) (Hα : 1 < α) (u : V) :
+ p u * (p u / q u) ^ (α.toEReal - 1).toReal =
+ (p u) ^ α * (q ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_2 | 7da023c589f9d173 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "ApproximateDP_of_zCDP_pos_lt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 141,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have Hε : 0 ≤ ε := by exact le_of_lt Hε_pos\n intro δ Hδ0 Hδ1\n generalize Dε' : (ε^2/2 + ε * (2*Real.... | [
{
"name": "ApproximateDP_HDP_bound",
"text": "lemma ApproximateDP_HDP_bound {U : Type*} (p q : PMF U) (Hac : AbsCts p q)\n (S : Set U) [DecidablePred (· ∈ S)] (ε' : ℝ) (Hε' : 0 ≤ ε') :\n ∑' (a : U), p a * ((if a ∈ S then (1 : ENNReal) else 0) *\n if ENNReal.elog (p a / q a) < (ENNReal.ofReal ε'... | [
{
"name": "ApproximateDP_of_zCDP_pos_lt_one",
"fan_in": 1,
"n_deps_direct": 8,
"n_deps_transitive": 10,
"n_lines": 150,
"n_chars": 5522,
"n_subproofs": 15,
"n_tactics": 110,
"cyclomatic": 2,
"n_automation": 13,
"n_rewrites": 33,
"n_structural": 26,
"automation_onl... | 10 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -296,6 +296,44 @@
· simp
· simp
+lemma ApproximateDP_HDP_bound {U : Type*} (p q : PMF U) (Hac : AbsCts p q)
+ (S : Set U) [DecidablePred (· ∈ S)] (ε' : ℝ) (Hε' : 0 ≤ ε') :
+ ∑' (a : U), p a * ((if a ∈ S then (1 : ENNReal) else 0) *
+ if ENNReal.elog (p a / q a) < (ENNReal.ofReal ε' : EReal) then... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_3 | 015a406602032daf | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "ApproximateDP_of_zCDP_pos_lt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 141,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have Hε : 0 ≤ ε := by exact le_of_lt Hε_pos\n intro δ Hδ0 Hδ1\n generalize Dε' : (ε^2/2 + ε * (2*Real.... | [
{
"name": "ApproximateDP_renyi_tsum_le",
"text": "lemma ApproximateDP_renyi_tsum_le [Countable U] (m₁ m₂ : PMF U)\n (Hm12 : AbsCts m₁ m₂) (Hm21 : AbsCts m₂ m₁)\n (ε : ℝ) (Hε : 0 ≤ ε) (α : ℝ) (Hα : 1 < α) (Hα' : 0 < α.toEReal - 1)\n (h : RenyiDivergence m₁ m₂ α ≤ ENNReal.ofReal (2⁻¹ * ε^2 * α)) :\n ... | [
{
"name": "ApproximateDP_of_zCDP_pos",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 15,
"n_chars": 524,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
... | 11 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -334,6 +334,59 @@
case G5 => linarith
exact le_of_lt H
+lemma ApproximateDP_renyi_tsum_le [Countable U] (m₁ m₂ : PMF U)
+ (Hm12 : AbsCts m₁ m₂) (Hm21 : AbsCts m₂ m₁)
+ (ε : ℝ) (Hε : 0 ≤ ε) (α : ℝ) (Hα : 1 < α) (Hα' : 0 < α.toEReal - 1)
+ (h : RenyiDivergence m₁ m₂ α ≤ ENNReal.ofReal (2⁻¹ * ε^2 * α))... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_4 | a3c79a5b1e076b05 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "ApproximateDP_of_zCDP_pos_lt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 141,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have Hε : 0 ≤ ε := by exact le_of_lt Hε_pos\n intro δ Hδ0 Hδ1\n generalize Dε' : (ε^2/2 + ε * (2*Real.... | [
{
"name": "ApproximateDP_renyi_tsum_le",
"text": "lemma ApproximateDP_renyi_tsum_le [Countable U] (m₁ m₂ : PMF U)\n (Hm12 : AbsCts m₁ m₂) (Hm21 : AbsCts m₂ m₁)\n (ε : ℝ) (Hε : 0 ≤ ε) (α : ℝ) (Hα : 1 < α) (Hα' : 0 < α.toEReal - 1)\n (h : RenyiDivergence m₁ m₂ α ≤ ENNReal.ofReal (2⁻¹ * ε^2 * α)) :\n ... | [
{
"name": "ApproximateDP_of_zCDP",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 22,
"n_chars": 752,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 6,
"automation_only": false,
"ma... | 12 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -334,6 +334,59 @@
case G5 => linarith
exact le_of_lt H
+lemma ApproximateDP_renyi_tsum_le [Countable U] (m₁ m₂ : PMF U)
+ (Hm12 : AbsCts m₁ m₂) (Hm21 : AbsCts m₂ m₁)
+ (ε : ℝ) (Hε : 0 ≤ ε) (α : ℝ) (Hα : 1 < α) (Hα' : 0 < α.toEReal - 1)
+ (h : RenyiDivergence m₁ m₂ α ≤ ENNReal.ofReal (2⁻¹ * ε^2 * α))... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_5 | 87e1e1dbecb320f5 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "ApproximateDP_of_zCDP",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain Hε | Hε' := LE.le.lt_or_eq Hε\n · intro δ a\n exact ApproximateDP_of_zCDP_pos m ε Hε h Hm δ a\n · intro ... | [
{
"name": "ApproximateDP_of_zCDP_pos",
"text": "/--\nObtain an approximate DP bound from a zCDP bound, when ε > 0\n-/\nlemma ApproximateDP_of_zCDP_pos [Countable U] (m : Mechanism T U)\n (ε : ℝ) (Hε_pos : 0 < ε) (h : zCDPBound m ((1/2) * ε^2)) (Hm : ACNeighbour m) :\n ∀ δ : NNReal, (0 < (δ : ℝ)) -> DP... | [
{
"name": "zCDP_ApproximateDP",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 14,
"n_lines": 23,
"n_chars": 672,
"n_subproofs": 2,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 5,
"automation_only": false,
"max_n... | 14 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -529,13 +529,28 @@
· exact mul_zero _
/--
+Obtain an approximate DP bound from a zCDP bound, when ε > 0
+-/
+lemma ApproximateDP_of_zCDP_pos [Countable U] (m : Mechanism T U)
+ (ε : ℝ) (Hε_pos : 0 < ε) (h : zCDPBound m ((1/2) * ε^2)) (Hm : ACNeighbour m) :
+ ∀ δ : NNReal, (0 < (δ : ℝ)) -> DP' m (ε^2/2 + ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_7 | 6005dc7163abbd3a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "A_jensen",
"depth": 1,
"n_commands": 0,
"n_lines": 69,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n have SC1 (b : Bool) : A_val ε b ≠ ⊤ := by cases b <;> simp [A_val]\n have SC2 (b : Bool) : (A_pmf ε p q Hqp x) b ≠ ⊤ := by\n ... | [
{
"name": "A_jensen_real",
"text": "/--\nJensen's inequality for the random variable A: real reduct\n-/\nlemma A_jensen_real (Hqp : ∀ x, ENNReal.ofReal (Real.exp (-ε)) ≤ p x / q x) {α : ℝ} (Hα : 1 < α) (x : U) :\n (∑'(b : Bool), (A_val ε b).toReal * (A_pmf ε p q Hqp x b).toReal) ^ α ≤ (∑'(b : Bool), ((A_... | [
{
"name": "A_jensen",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 76,
"n_chars": 2194,
"n_subproofs": 3,
"n_tactics": 69,
"cyclomatic": 5,
"n_automation": 8,
"n_rewrites": 13,
"n_structural": 39,
"automation_only": false,
"max_nesting":... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -262,12 +262,116 @@
· rfl
/--
+Jensen's inequality for the random variable A: real reduct
+-/
+lemma A_jensen_real (Hqp : ∀ x, ENNReal.ofReal (Real.exp (-ε)) ≤ p x / q x) {α : ℝ} (Hα : 1 < α) (x : U) :
+ (∑'(b : Bool), (A_val ε b).toReal * (A_pmf ε p q Hqp x b).toReal) ^ α ≤ (∑'(b : Bool), ((A_val ε b).to... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_8 | 9831ce7325777472 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 2 | [
{
"theorem_name": "B_eval_false",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have H1 : (1 - (B ε p q Hqp) false) = B ε p q Hqp true := by\n apply ENNReal.sub_eq_of_eq_add ?G1\n case G1 => apply PM... | [
{
"name": "B_eval_open",
"text": "/--\nFormula for B which shows up in the main derivation\n-/\nlemma B_eval_open (Hqp : ∀ x, ENNReal.ofReal (Real.exp (-ε)) ≤ p x / q x)\n (b : Bool) : B ε p q Hqp b = ∑'(x : U), A_pmf ε p q Hqp x b * q x := by\n unfold B\n simp\n apply tsum_congr\n intro\n rw [mul_c... | [
{
"name": "B_eval_false",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 56,
"n_chars": 1871,
"n_subproofs": 4,
"n_tactics": 44,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 22,
"n_structural": 7,
"automation_only": false,
"max_nestin... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -374,6 +374,17 @@
noncomputable def B (Hqp : ∀ x, ENNReal.ofReal (Real.exp (-ε)) ≤ p x / q x) : PMF Bool := q >>= A_pmf ε p q Hqp
+/--
+Formula for B which shows up in the main derivation
+-/
+lemma B_eval_open (Hqp : ∀ x, ENNReal.ofReal (Real.exp (-ε)) ≤ p x / q x)
+ (b : Bool) : B ε p q Hqp b = ∑'(x : U), ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_9 | f199baa487c423c3 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 2 | [
{
"theorem_name": "B_eval_true",
"depth": 1,
"n_commands": 0,
"n_lines": 58,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have H1 : (1 - (B ε p q Hqp) false) = B ε p q Hqp true := by\n apply ENNReal.sub_eq_of_eq_add ?G1\n case G1 => apply PMF... | [
{
"name": "B_eval_false",
"text": "/--\nclosed form for B false\n-/\nlemma B_eval_false (Hε : 0 < ε) (Hqp : ∀ x, ENNReal.ofReal (Real.exp (-ε)) ≤ p x / q x)\n (Hpq : ∀ x, (p x / q x ≤ ENNReal.ofReal (Real.exp ε))) (Hac : AbsCts p q) :\n B ε p q Hqp false = (ENNReal.ofReal (Real.exp ε) - 1) / (ENNReal.... | [
{
"name": "B_eval_true",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 65,
"n_chars": 1845,
"n_subproofs": 5,
"n_tactics": 56,
"cyclomatic": 3,
"n_automation": 11,
"n_rewrites": 23,
"n_structural": 11,
"automation_only": false,
"max_nesti... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -503,12 +503,122 @@
ring_nf
/--
+closed form for B false
+-/
+lemma B_eval_false (Hε : 0 < ε) (Hqp : ∀ x, ENNReal.ofReal (Real.exp (-ε)) ≤ p x / q x)
+ (Hpq : ∀ x, (p x / q x ≤ ENNReal.ofReal (Real.exp ε))) (Hac : AbsCts p q) :
+ B ε p q Hqp false = (ENNReal.ofReal (Real.exp ε) - 1) / (ENNReal.ofReal (Re... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_10 | eaeecee287c6d03e | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 2 | [
{
"theorem_name": "lemma_sinh_sub",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n calc Real.sinh (x - y)\n _ = (Real.exp (x - y) - Real.exp (-(x-y))) / 2 := by\n rw [Real.sinh_eq]\n _ = ((Real.exp ... | [
{
"name": "lemma_cosh_add",
"text": "lemma lemma_cosh_add {w z : ℝ} : Real.cosh (w + z) = Real.cosh w * Real.cosh z * (1 + Real.tanh w * Real.tanh z) :=\n let L {a : ℝ} : Real.sinh a = Real.cosh a * Real.tanh a := by\n rw [Real.tanh_eq_sinh_div_cosh]\n rw [division_def, mul_comm, mul_assoc]\n rw [... | [
{
"name": "lemma_sinh_sub",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 37,
"n_chars": 1128,
"n_subproofs": 2,
"n_tactics": 34,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 17,
"n_structural": 2,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -627,15 +627,81 @@
section sinh_inequality
+lemma lemma_cosh_add {w z : ℝ} : Real.cosh (w + z) = Real.cosh w * Real.cosh z * (1 + Real.tanh w * Real.tanh z) :=
+ let L {a : ℝ} : Real.sinh a = Real.cosh a * Real.tanh a := by
+ rw [Real.tanh_eq_sinh_div_cosh]
+ rw [division_def, mul_comm, mul_assoc]
+ r... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_11 | 2d34080db8802b4d | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "lemma_step_1",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [lemma_sinh_sub]\n rw [lemma_sub_sinh]\n rw [mul_div_mul_comm]\n rw [div_self]\n · simp\n · apply C_ne_zero\n linar... | [
{
"name": "C_ne_zero",
"text": "lemma C_ne_zero (Hyx : y < x) : C x y ≠ 0 := by\n unfold C\n repeat apply mul_ne_zero\n · simp\n · apply Real.sinh_ne_zero.mpr\n linarith\n · linarith [Real.cosh_pos (x / 2)]\n · linarith [Real.cosh_pos (y / 2)]\n\n",
"fan_in": 1,
"n_lines": 10,
"n_chars"... | [
{
"name": "lemma_step_1",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 10,
"n_chars": 246,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -703,13 +703,23 @@
rw [lemma_cosh_add]
linarith
+lemma C_ne_zero (Hyx : y < x) : C x y ≠ 0 := by
+ unfold C
+ repeat apply mul_ne_zero
+ · simp
+ · apply Real.sinh_ne_zero.mpr
+ linarith
+ · linarith [Real.cosh_pos (x / 2)]
+ · linarith [Real.cosh_pos (y / 2)]
+
lemma lemma_step_1 (Hyx : y ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_12 | dc807b78da1d8c07 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "t_le_one",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold t\n conv =>\n enter [2]\n rw [<- mul_one 1]\n apply (mul_lt_mul'' (tanh_lt_1 (x / 2)) (tanh_lt_1 (y / 2)))\n · ap... | [
{
"name": "tanh_nonneg",
"text": "lemma tanh_nonneg {w : ℝ} (HW : 0 ≤ w) : 0 ≤ Real.tanh w := by\n rw [Real.tanh_eq_sinh_div_cosh]\n apply div_nonneg\n · exact Real.sinh_nonneg_iff.mpr HW\n · exact (LT.lt.le (Real.cosh_pos w))\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 202,
"n_subproofs... | [
{
"name": "t_le_one",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 256,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 3,
"automation_only": false,
"max_nesting": 4
... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -731,14 +731,22 @@
· apply Real.cosh_pos
-- Upstream?
+lemma tanh_nonneg {w : ℝ} (HW : 0 ≤ w) : 0 ≤ Real.tanh w := by
+ rw [Real.tanh_eq_sinh_div_cosh]
+ apply div_nonneg
+ · exact Real.sinh_nonneg_iff.mpr HW
+ · exact (LT.lt.le (Real.cosh_pos w))
+
lemma t_le_one (Hy : 0 ≤ y) (Hyx : y < x) : t x y < 1 :=... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_13 | 4984a9c2e8dfb021 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "lemma_step_2",
"depth": 1,
"n_commands": 0,
"n_lines": 49,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply div_le_of_le_mul₀\n · linarith [t_le_one x y Hy Hyx]\n · apply Real.exp_nonneg\n rw [mul_sub]\n simp\n apply (add_... | [
{
"name": "t_le_one",
"text": "lemma t_le_one (Hy : 0 ≤ y) (Hyx : y < x) : t x y < 1 := by\n unfold t\n conv =>\n enter [2]\n rw [<- mul_one 1]\n apply (mul_lt_mul'' (tanh_lt_1 (x / 2)) (tanh_lt_1 (y / 2)))\n · apply tanh_nonneg\n linarith\n · apply tanh_nonneg\n linarith\n\n\n",
"fan_i... | [
{
"name": "lemma_step_2",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 51,
"n_chars": 1364,
"n_subproofs": 3,
"n_tactics": 49,
"cyclomatic": 2,
"n_automation": 11,
"n_rewrites": 19,
"n_structural": 11,
"automation_only": false,
"max_nest... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -737,9 +737,20 @@
· exact Real.sinh_nonneg_iff.mpr HW
· exact (LT.lt.le (Real.cosh_pos w))
+lemma t_le_one (Hy : 0 ≤ y) (Hyx : y < x) : t x y < 1 := by
+ unfold t
+ conv =>
+ enter [2]
+ rw [<- mul_one 1]
+ apply (mul_lt_mul'' (tanh_lt_1 (x / 2)) (tanh_lt_1 (y / 2)))
+ · apply tanh_nonneg
+ lina... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_14 | f62c66015b14e7a3 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 2 | [
{
"theorem_name": "tanh_lt_id_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 38,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let f (x : ℝ) := x - Real.tanh x\n suffices 0 * (x - 0) ≤ f x - f 0 by\n dsimp [f] at this\n simp at this\n tr... | [
{
"name": "deriv.deriv_tanh",
"text": "lemma deriv.deriv_tanh (x : ℝ) : deriv Real.tanh x = 1 / (Real.cosh x) ^ 2 := by\n have Hcne : Real.cosh x ≠ 0 := by have := Real.cosh_pos x; linarith\n have Htanh_eq : Real.tanh = Real.sinh / Real.cosh := by\n funext z; simp [Real.tanh_eq_sinh_div_cosh, Pi.div_ap... | [
{
"name": "tanh_lt_id_nonneg",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 42,
"n_chars": 1229,
"n_subproofs": 4,
"n_tactics": 39,
"cyclomatic": 1,
"n_automation": 11,
"n_rewrites": 4,
"n_structural": 14,
"automation_only": false,
"max_... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -820,6 +820,16 @@
have _ := Real.cosh_pos z
linarith
+lemma deriv.deriv_tanh (x : ℝ) : deriv Real.tanh x = 1 / (Real.cosh x) ^ 2 := by
+ have Hcne : Real.cosh x ≠ 0 := by have := Real.cosh_pos x; linarith
+ have Htanh_eq : Real.tanh = Real.sinh / Real.cosh := by
+ funext z; simp [Real.tanh_eq_sinh_d... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_15 | dc7ceb8bf8c98b11 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 3 | [
{
"theorem_name": "tanh_lt_id_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 38,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let f (x : ℝ) := x - Real.tanh x\n suffices 0 * (x - 0) ≤ f x - f 0 by\n dsimp [f] at this\n simp at this\n tr... | [
{
"name": "Differentiable.differentiable_tanh",
"text": "lemma Differentiable.differentiable_tanh : Differentiable ℝ Real.tanh := by\n conv =>\n enter [2, y]\n rw [Real.tanh_eq_sinh_div_cosh]\n apply Differentiable.div\n · apply Real.differentiable_sinh\n · apply Real.differentiable_cosh\n · int... | [
{
"name": "lemma_step_3_aux_differentiable",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 926,
"n_subproofs": 2,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 11,
"automation_only": fals... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -798,6 +798,17 @@
· linarith
· linarith
+lemma Differentiable.differentiable_tanh : Differentiable ℝ Real.tanh := by
+ conv =>
+ enter [2, y]
+ rw [Real.tanh_eq_sinh_div_cosh]
+ apply Differentiable.div
+ · apply Real.differentiable_sinh
+ · apply Real.differentiable_cosh
+ · intro z
+ have _ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_16 | 1be363984ec7ff8c | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 2 | [
{
"theorem_name": "lemma_step_3_aux_continuous",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (lemma_step_3_aux_differentiable x).continuous",
"n_chars": 49,
"n_subproofs": 0,
"n_tactics": 1,
... | [
{
"name": "lemma_step_3_aux_differentiable",
"text": "lemma lemma_step_3_aux_differentiable (x : ℝ) :\n Differentiable ℝ (fun z : ℝ => Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)) := by\n apply Differentiable.sub\n · have Hfunc : (fun y : ℝ => Real.tanh (x * y / 4)) =\n ... | [
{
"name": "lemma_step_3_aux_continuous",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 193,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -869,8 +869,31 @@
trivial
· trivial
+lemma lemma_step_3_aux_differentiable (x : ℝ) :
+ Differentiable ℝ (fun z : ℝ => Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)) := by
+ apply Differentiable.sub
+ · have Hfunc : (fun y : ℝ => Real.tanh (x * y / 4)) =
+ ((fun (y : ℝ) ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_17 | d2d50cbc9c80e448 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "lemma_step_3",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let f (z : ℝ) := Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)\n suffices 0 ≤ f y by\n dsimp [f] at this... | [
{
"name": "lemma_step_3_aux_continuous",
"text": "lemma lemma_step_3_aux_continuous (x : ℝ) :\n Continuous (fun z : ℝ => Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)) :=\n (lemma_step_3_aux_differentiable x).continuous\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 193,
"n_... | [
{
"name": "lemma_step_3",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 7,
"n_lines": 29,
"n_chars": 872,
"n_subproofs": 4,
"n_tactics": 26,
"cyclomatic": 2,
"n_automation": 12,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nesting... | 7 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -891,6 +891,10 @@
· apply Differentiable.mul_const
exact differentiable_id
+lemma lemma_step_3_aux_continuous (x : ℝ) :
+ Continuous (fun z : ℝ => Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)) :=
+ (lemma_step_3_aux_differentiable x).continuous
+
lemma lemma_step_3_deriv_nonneg (x... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_18 | a2dc4de1732c3dfa | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 3 | [
{
"theorem_name": "ofDP_bound_SC1",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ENNReal.mul_ne_top\n · exact ENNReal.rpow_ne_top_of_nonneg Hα ENNReal.ofReal_ne_top\n apply lt_top_iff_ne_top.mp\n ... | [
{
"name": "ofDP_bound_SC0",
"text": "lemma ofDP_bound_SC0 (ε : NNReal) (Hε : 0 < ε) :\n ENNReal.ofReal (Real.exp ↑ε) - ENNReal.ofReal (Real.exp (-↑ε)) ≠ 0 := by\n apply ne_of_gt\n simp\n apply ENNReal.ofReal_lt_ofReal_iff'.mpr\n refine ⟨?_, Real.exp_pos _⟩\n apply Real.exp_lt_exp.mpr\n simp\n exac... | [
{
"name": "ofDP_bound_SC1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 498,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -1079,6 +1079,16 @@
· simp
linarith
+lemma ofDP_bound_SC0 (ε : NNReal) (Hε : 0 < ε) :
+ ENNReal.ofReal (Real.exp ↑ε) - ENNReal.ofReal (Real.exp (-↑ε)) ≠ 0 := by
+ apply ne_of_gt
+ simp
+ apply ENNReal.ofReal_lt_ofReal_iff'.mpr
+ refine ⟨?_, Real.exp_pos _⟩
+ apply Real.exp_lt_exp.mpr
+ simp
+ exa... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_19 | 75d071aae18c3bd7 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "sinh_inequality",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Temp usage of hypothesis so Lean doesn't freak out\n have _ := Hy\n have _ := Hx\n rw [lemma_step_1 _ _ Hyx]\n apply... | [
{
"name": "lemma_step_3",
"text": "lemma lemma_step_3 (Hy : 0 ≤ y) (Hyx : y < x) (Hx : x ≤ 2) : Real.tanh (x / 2) * Real.tanh (y / 2) ≤ Real.tanh (x * y / 4) := by\n let f (z : ℝ) := Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)\n suffices 0 ≤ f y by\n dsimp [f] at this\n linarith\n... | [
{
"name": "ofDP_bound",
"fan_in": 1,
"n_deps_direct": 12,
"n_deps_transitive": 35,
"n_lines": 263,
"n_chars": 7759,
"n_subproofs": 21,
"n_tactics": 219,
"cyclomatic": 12,
"n_automation": 42,
"n_rewrites": 55,
"n_structural": 77,
"automation_only": false,
"max_... | 34 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -1008,8 +1008,42 @@
· linarith
apply sq_nonneg
+lemma lemma_step_3 (Hy : 0 ≤ y) (Hyx : y < x) (Hx : x ≤ 2) : Real.tanh (x / 2) * Real.tanh (y / 2) ≤ Real.tanh (x * y / 4) := by
+ let f (z : ℝ) := Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)
+ suffices 0 ≤ f y by
+ dsimp [f] at this... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5997d3a636e9_20 | 679053a606636d50 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/DP.lean | DP | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 48 | 1 | [
{
"theorem_name": "sinh_inequality",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Temp usage of hypothesis so Lean doesn't freak out\n have _ := Hy\n have _ := Hx\n rw [lemma_step_1 _ _ Hyx]\n apply... | [
{
"name": "lemma_step_3",
"text": "lemma lemma_step_3 (Hy : 0 ≤ y) (Hyx : y < x) (Hx : x ≤ 2) : Real.tanh (x / 2) * Real.tanh (y / 2) ≤ Real.tanh (x * y / 4) := by\n let f (z : ℝ) := Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)\n suffices 0 ≤ f y by\n dsimp [f] at this\n linarith\n... | [
{
"name": "ofDP",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 36,
"n_lines": 5,
"n_chars": 180,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": 2
}
] | 34 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Algebra.Group.Basic
impor... | @@ -1008,8 +1008,42 @@
· linarith
apply sq_nonneg
+lemma lemma_step_3 (Hy : 0 ≤ y) (Hyx : y < x) (Hx : x ≤ 2) : Real.tanh (x / 2) * Real.tanh (y / 2) ≤ Real.tanh (x * y / 4) := by
+ let f (z : ℝ) := Real.tanh (x * z / 4) - Real.tanh (x / 2) * Real.tanh (z / 2)
+ suffices 0 ≤ f y by
+ dsimp [f] at this... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_0 | c5bc8ef48e7f189c | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "dropLast_append_getLastI",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [getLastI_eq_getLast _ H]\n apply List.dropLast_append_getLast H",
"n_chars": 73,
"n_subproofs": 0,
... | [
{
"name": "getLastI_eq_getLast",
"text": "lemma getLastI_eq_getLast (L : List ℤ) (H : L ≠ []) : L.getLastI = L.getLast H := by\n rw [List.getLastI_eq_getLast?_getD]\n rw [List.getLast?_eq_getLast_of_ne_nil H]\n rfl\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 178,
"n_subproofs": 0,
"n_... | [
{
"name": "dropLast_append_getLastI",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 171,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -59,8 +59,15 @@
intro a
apply le_iSup
-lemma dropLast_append_getLastI (L : List ℤ) (H : L ≠ []) : L.dropLast ++ [L.getLastI] = L := sorry
+lemma getLastI_eq_getLast (L : List ℤ) (H : L ≠ []) : L.getLastI = L.getLast H := by
+ rw [List.getLastI_eq_getLast?_getD]
+ rw [List.getLast?_eq_getLast_of_ne_nil H]
+... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_1 | 346b4b4701ece8aa | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 4 | [
{
"theorem_name": "vector_sum_singleton",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply @tsum_eq_tsum_of_ne_zero_bij\n case i =>\n simp [Function.support]\n exact fun x => ⟨ [x.1], by simp ⟩\n... | [
{
"name": "tsum_eq_tsum_of_ne_zero_bij",
"text": "/--\nBijection-style tsum equality. Local replacement for a previously-removed mathlib\nlemma of the same name. Stated in terms of `Equiv.tsum_eq`.\n-/\ntheorem tsum_eq_tsum_of_ne_zero_bij {α : Type*} [AddCommMonoid α] [TopologicalSpace α]\n {β γ : Type*}... | [
{
"name": "vector_sum_singleton",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 523,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -20,6 +20,38 @@
rw [← Summable.hasSum_iff ENNReal.summable]
exact p.2
+/--
+Bijection-style tsum equality. Local replacement for a previously-removed mathlib
+lemma of the same name. Stated in terms of `Equiv.tsum_eq`.
+-/
+theorem tsum_eq_tsum_of_ne_zero_bij {α : Type*} [AddCommMonoid α] [TopologicalSpace α... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_2 | 8eb10c578c71d925 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 6 | [
{
"theorem_name": "sv1_loop_ub",
"depth": 1,
"n_commands": 0,
"n_lines": 48,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction cut with\n | zero => simp [probWhileCut]\n | succ cut' IH =>\n intro L v0\n simp [probWhileCut, probWhileFun... | [
{
"name": "SPMF_sum_one",
"text": "lemma SPMF_sum_one (p : SPMF ℤ) : ∑' (a : ℤ), p a = 1 := by\n rw [← Summable.hasSum_iff ENNReal.summable]\n exact p.2\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 127,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n... | [
{
"name": "sv1_loop_ub",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 51,
"n_chars": 1534,
"n_subproofs": 0,
"n_tactics": 47,
"cyclomatic": 3,
"n_automation": 12,
"n_rewrites": 9,
"n_structural": 13,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -16,6 +16,10 @@
variable {sv_T : Type}
+lemma SPMF_sum_one (p : SPMF ℤ) : ∑' (a : ℤ), p a = 1 := by
+ rw [← Summable.hasSum_iff ENNReal.summable]
+ exact p.2
+
/--
Bijection-style tsum equality. Local replacement for a previously-removed mathlib
lemma of the same name. Stated in terms of `Equiv.tsum_eq`.
@... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_3 | 941895d7a7f96f16 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "cone_left_edge_constancy",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro Hlen Hcone\n -- cut > 0 due to cone\n cases cut with\n | zero =>\n exfalso\n simp [cone_of_possibi... | [
{
"name": "external_to_cone_zero",
"text": "lemma external_to_cone_zero :\n (¬ cone_of_possibility cut initial hist) ->\n probWhileCut (sv1_aboveThreshC qs T τ data) (sv1_aboveThreshF ε₁ ε₂) cut (initial, v0) (hist, vk) = 0 := by\n revert initial v0 vk\n induction cut\n · simp [probWhileCut]\n · n... | [
{
"name": "cone_left_edge_constancy",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 52,
"n_chars": 1564,
"n_subproofs": 0,
"n_tactics": 39,
"cyclomatic": 6,
"n_automation": 10,
"n_rewrites": 7,
"n_structural": 13,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -424,6 +424,36 @@
probWhileCut (sv1_aboveThreshC qs T τ data) (sv1_aboveThreshF ε₁ ε₂) cut (initial, v0) (hist, vk)
-- All points outside of the cone are zero
+lemma external_to_cone_zero :
+ (¬ cone_of_possibility cut initial hist) ->
+ probWhileCut (sv1_aboveThreshC qs T τ data) (sv1_aboveThreshF... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_4 | 1e35c1db7ec787ca | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "cone_constancy",
"depth": 1,
"n_commands": 0,
"n_lines": 80,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Need theorem to be true for all initial states, since this will increase during the induction\n -- v0 and vk will also ... | [
{
"name": "cone_left_edge_constancy",
"text": "lemma cone_left_edge_constancy {qs : sv_query sv_T} {T : ℤ} {ε₁ ε₂ : ℕ+} {τ : ℤ} {data : List sv_T} {v0 vk : ℤ} (cut : ℕ) (initial hist : List ℤ) :\n hist.length = initial.length ->\n cone_of_possibility cut initial hist ->\n @constancy_at _ _ _ qs T ε... | [
{
"name": "sv2_sv3_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 63,
"n_chars": 1586,
"n_subproofs": 1,
"n_tactics": 50,
"cyclomatic": 9,
"n_automation": 9,
"n_rewrites": 10,
"n_structural": 25,
"automation_only": false,
"max_nesting... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -454,6 +454,57 @@
simp_all [cone_of_possibility]
-- Base case: left edge of the cone satisfies constancy
+lemma cone_left_edge_constancy {qs : sv_query sv_T} {T : ℤ} {ε₁ ε₂ : ℕ+} {τ : ℤ} {data : List sv_T} {v0 vk : ℤ} (cut : ℕ) (initial hist : List ℤ) :
+ hist.length = initial.length ->
+ cone_of_pos... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_5 | 61aba5b260b2bf95 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "sv4_presample_eval'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have X := sv4_presample_eval ε₁ ε₂ n ⟨ List.reverse s, by simp ⟩\n simp only [List.reverse_reverse, Subtype.coe_eta] a... | [
{
"name": "sv4_presample_eval",
"text": "lemma sv4_presample_eval (ε₁ ε₂ : ℕ+) (n : ℕ) (s : { l : List ℤ // List.length l = n }) :\n sv4_presample ε₁ ε₂ n ⟨ List.reverse s, by simp ⟩ = List.foldl (fun acc b => acc * (privNoiseGuess ε₁ ε₂ b)) 1 s.1 := by\n rcases s with ⟨ s, Hs ⟩\n simp\n revert n\n i... | [
{
"name": "sv4_presample_eval'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 428,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -728,8 +728,74 @@
def len_list_append_rev {m n : ℕ} (x : { l : List ℤ // l.length = m }) (y: { l : List ℤ // l.length = n }) : { l : List ℤ // l.length = n + m } :=
⟨ x.1 ++ y.1 , by simp [add_comm] ⟩
+lemma sv4_presample_eval (ε₁ ε₂ : ℕ+) (n : ℕ) (s : { l : List ℤ // List.length l = n }) :
+ sv4_presample... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_6 | 1094f1247c8163fb | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "sv5_sv6_loop_eq_point",
"depth": 1,
"n_commands": 0,
"n_lines": 32,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n revert past pres eval\n induction future\n · intro eval past pres H1 H2\n symm\n simp at H1\n apply (sv5_... | [
{
"name": "sv6_loop_ind",
"text": "lemma sv6_loop_ind (qs : sv_query sv_T) (T : ℤ) (τ : ℤ) (l : List sv_T) (point : ℕ) (past ff: List ℤ) (pres f: ℤ) :\n (sv4_aboveThreshC qs T τ l ((past, pres), f :: ff) = true) ->\n List.length (past ++ [pres] ++ f :: ff) = point + 1 ->\n (sv6_loop qs T τ l... | [
{
"name": "sv5_sv6_loop_eq_point",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 38,
"n_chars": 1251,
"n_subproofs": 0,
"n_tactics": 32,
"cyclomatic": 4,
"n_automation": 11,
"n_rewrites": 6,
"n_structural": 8,
"automation_only": false,
"m... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -1346,6 +1346,22 @@
split_ifs <;> simp_all
omit [DPSystem ℕ] [DPNoise dps] in
+lemma sv6_loop_ind (qs : sv_query sv_T) (T : ℤ) (τ : ℤ) (l : List sv_T) (point : ℕ) (past ff: List ℤ) (pres f: ℤ) :
+ (sv4_aboveThreshC qs T τ l ((past, pres), f :: ff) = true) ->
+ List.length (past ++ [pres] ++ f :: f... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_8 | 39d0d82b7ddaf0ee | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "sv8_sv9_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply SLang.ext\n intro point\n unfold sv8_aboveThresh\n unfold sv9_aboveThresh\n simp\n split\n · simp\n · simp\n co... | [
{
"name": "tsum_comm_mul_left",
"text": "lemma tsum_comm_mul_left {α β : Type*} (f : α → ENNReal) (g : β → ENNReal) (h : α → β → ENNReal) :\n ∑' a, f a * ∑' b, g b * h a b = ∑' b, g b * ∑' a, f a * h a b := by\n conv =>\n lhs\n enter [1, a]\n rw [← ENNReal.tsum_mul_left]\n enter [1, b]\n ... | [
{
"name": "sv8_sv9_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 404,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 6,
"n_structural": 4,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -76,6 +76,17 @@
simp at H
simp
+lemma tsum_comm_mul_left {α β : Type*} (f : α → ENNReal) (g : β → ENNReal) (h : α → β → ENNReal) :
+ ∑' a, f a * ∑' b, g b * h a b = ∑' b, g b * ∑' a, f a * h a b := by
+ conv =>
+ lhs
+ enter [1, a]
+ rw [← ENNReal.tsum_mul_left]
+ enter [1, b]
+ rw [mul_... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_9 | f347ac9ffed4f2b2 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 2 | [
{
"theorem_name": "sv1_lb_advance",
"depth": 1,
"n_commands": 0,
"n_lines": 61,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv =>\n rhs\n enter [1, x1, 1, x2]\n unfold probWhileCut\n unfold probWhileFunctional\n simp\n split\n ·... | [
{
"name": "ENNReal.tsum_lb_single",
"text": "lemma ENNReal.tsum_lb_single (x : T) (f : T -> ENNReal) (l : ENNReal) :\n l ≤ f x -> l ≤ ∑' (a : T), f a := by\n intro H\n apply le_trans H\n apply ENNReal.le_tsum\n\n",
"fan_in": 2,
"n_lines": 7,
"n_chars": 174,
"n_subproofs": 0,
"n_ta... | [
{
"name": "sv1_lb",
"fan_in": 1,
"n_deps_direct": 10,
"n_deps_transitive": 11,
"n_lines": 297,
"n_chars": 9016,
"n_subproofs": 12,
"n_tactics": 237,
"cyclomatic": 7,
"n_automation": 33,
"n_rewrites": 56,
"n_structural": 90,
"automation_only": false,
"max_nesti... | 11 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -87,6 +87,12 @@
rw [ENNReal.tsum_comm]
simp_rw [ENNReal.tsum_mul_left]
+lemma ENNReal.tsum_lb_single (x : T) (f : T -> ENNReal) (l : ENNReal) :
+ l ≤ f x -> l ≤ ∑' (a : T), f a := by
+ intro H
+ apply le_trans H
+ apply ENNReal.le_tsum
+
lemma ENNReal.tsum_split (P : T -> Prop) (f : T -> ENNReal) :
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2258aec67b29_10 | ea1b2e2f83135ad2 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Properties.lean | Properties | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "sv1_lb",
"depth": 1,
"n_commands": 0,
"n_lines": 293,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [sv1_aboveThresh, bind, pure, bind_apply]\n -- Push the sum over s inwards\n conv =>\n rhs\n rw [ENNReal.tsum_co... | [
{
"name": "ite_conv_left",
"text": "lemma ite_conv_left {P : Prop} {D} {a b c : ENNReal} (H : a = c) : @ite _ P D a b = @ite _ P D c b := by\n split <;> trivial\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 126,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,... | [
{
"name": "sv1_hasSum_one",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 14,
"n_lines": 9,
"n_chars": 416,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting... | 14 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Code
noncomputable section
open Classic... | @@ -150,6 +150,9 @@
def geo_cdf (β : ENNReal) (n : ℕ) : ENNReal := 1 - (1 - β)^n
+lemma ite_conv_left {P : Prop} {D} {a b c : ENNReal} (H : a = c) : @ite _ P D a b = @ite _ P D c b := by
+ split <;> trivial
+
lemma ite_lemma_1 {P : Prop} {D} {f : T -> ENNReal} : ∑'(a : T), @ite _ P D (f a) 0 = @ite _ P D (∑'(a :... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_637af78ef56e_0 | 6fbd4d6316c11eb2 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Pure/Postprocessing.lean | Postprocessing | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "PureDP_PostProcess",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [PureDP] at *\n apply privPostProcess_DP_bound h",
"n_chars": 59,
"n_subproofs": 0,
"n_tactics": 3,
... | [
{
"name": "privPostProcess_DP_bound",
"text": "lemma privPostProcess_DP_bound {nq : Mechanism T U} {ε : NNReal} (h : PureDP nq ε) (f : U → V) :\n DP (privPostProcess nq f) ε := by\n simp [PureDP] at *\n rw [event_eq_singleton] at *\n simp [DP_singleton] at *\n intros l₁ l₂ neighbours x\n replace h := ... | [
{
"name": "PureDP_PostProcess",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 285,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Pure.DP
import SampCert.DifferentialPrivacy.Generic
import Mathlib.Data.Set.Defs
import Mathlib.Data.Se... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Pure.DP
import SampCert.DifferentialPrivacy.Generic
import Mathlib.Data.Set.Defs
import Mathlib.Data.Se... | @@ -20,11 +20,36 @@
namespace SLang
+lemma privPostProcess_DP_bound {nq : Mechanism T U} {ε : NNReal} (h : PureDP nq ε) (f : U → V) :
+ DP (privPostProcess nq f) ε := by
+ simp [PureDP] at *
+ rw [event_eq_singleton] at *
+ simp [DP_singleton] at *
+ intros l₁ l₂ neighbours x
+ replace h := h l₁ l₂ neighbour... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_778c835dbc80_0 | 6429f09fb7ce9624 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Foundations/Monad.lean | Monad | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "bind_pure",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n SLang.ext fun x => (bind_apply _ _ _).trans (_root_.trans\n (tsum_eq_single x fun y hy => by rw [pure_apply_of_ne _ _ hy.symm, mu... | [
{
"name": "pure_apply_of_ne",
"text": "theorem pure_apply_of_ne (h : a' ≠ a) : probPure a a' = 0 :=\n if_neg h\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 75,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"a... | [
{
"name": "bind_pure",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 239,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 4
... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
/-!
# Monad Properties
This file contains the standard monadic equations for ``SLang``.
-/
noncomputable section
... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
/-!
# Monad Properties
This file contains the standard monadic equations for ``SLang``.
-/
noncomputable section
... | @@ -42,6 +42,9 @@
theorem pure_apply_self : probPure a a = 1 :=
if_pos rfl
+theorem pure_apply_of_ne (h : a' ≠ a) : probPure a a' = 0 :=
+ if_neg h
+
variable (p : SLang α) (f : α → SLang β) (g : β → SLang γ)
@[simp]
@@ -55,7 +58,10 @@
simp [this]
@[simp]
-theorem bind_pure : p.probBind probPure = p :=... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_0 | 404a2e40872b85d3 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 2 | [
{
"theorem_name": "DiscreteLaplaceSampleLoopIn1_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 55,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [DiscreteLaplaceSampleLoopIn1_apply_pre, DiscreteLaplaceSampleLoopIn1Aux_apply_true]\n simp only [s... | [
{
"name": "DiscreteLaplaceSampleLoopIn1Aux_apply_true",
"text": "theorem DiscreteLaplaceSampleLoopIn1Aux_apply_true (t : PNat) (n : ℕ) :\n DiscreteLaplaceSampleLoopIn1Aux t (n, true)\n = if n < t then ENNReal.ofReal (rexp (- (n / t))) / t else 0 := by\n simp only [DiscreteLaplaceSampleLoopIn1Aux, B... | [
{
"name": "DiscreteLaplaceSampleLoopIn1_apply",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 60,
"n_chars": 2512,
"n_subproofs": 6,
"n_tactics": 63,
"cyclomatic": 1,
"n_automation": 14,
"n_rewrites": 25,
"n_structural": 5,
"automation_only":... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -70,6 +70,17 @@
intro a; rw [← tsum_bool, BernoulliExpNegSample_normalizes]
simp_rw [hnorm, mul_one, UniformSample_normalizes]
+theorem DiscreteLaplaceSampleLoopIn1Aux_apply_true (t : PNat) (n : ℕ) :
+ DiscreteLaplaceSampleLoopIn1Aux t (n, true)
+ = if n < t then ENNReal.ofReal (rexp (- (n / t))) /... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_1 | b89e107af747087a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "avoid_double_counting",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hr_lt_one : ENNReal.ofReal (rexp (-(↑↑den / ↑↑num))) < 1 := by\n apply ENNReal.ofReal_lt_one.mpr\n rw [ex... | [
{
"name": "avoid_double_counting_algebra",
"text": "theorem avoid_double_counting_algebra (r c : ENNReal) (hr_ne_one : 1 - r ≠ 0)\n (hr_ne_top : 1 - r ≠ ⊤) :\n (∑' n : ℕ, r ^ n * (1 - r) * c) + (∑' n : ℕ, r ^ (n + 1) * (1 - r) * c) = c * (1 + r) := by\n simp_rw [pow_succ, mul_assoc _ r _, mul_comm r ... | [
{
"name": "avoid_double_counting",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 974,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -262,10 +262,34 @@
trivial
· simp
+theorem avoid_double_counting_algebra (r c : ENNReal) (hr_ne_one : 1 - r ≠ 0)
+ (hr_ne_top : 1 - r ≠ ⊤) :
+ (∑' n : ℕ, r ^ n * (1 - r) * c) + (∑' n : ℕ, r ^ (n + 1) * (1 - r) * c) = c * (1 + r) := by
+ simp_rw [pow_succ, mul_assoc _ r _, mul_comm r _, ← mul_assoc, ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_2 | 32b09da14d33b26f | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "DiscreteLaplaceSample_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 69,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hA : 0 ≤ rexp (-(↑↑den / ↑↑num)) := exp_nonneg _\n have hB : 0 ≤ rexp (↑↑den / ↑↑num) := exp_nonneg _\n ... | [
{
"name": "avoid_double_counting",
"text": "theorem avoid_double_counting (num den : PNat) :\n (∑' (x : Bool × ℕ),\n if x.1 = true → ¬x.2 = 0 then DiscreteLaplaceSampleLoop num den x else 0)\n = (((2 : ℕ+) : ENNReal))⁻¹ * (1 + ENNReal.ofReal (rexp (-(↑↑den / ↑↑num)))) := by\n have hr_lt_one ... | [
{
"name": "DiscreteLaplaceSample_apply",
"fan_in": 2,
"n_deps_direct": 10,
"n_deps_transitive": 12,
"n_lines": 76,
"n_chars": 4404,
"n_subproofs": 13,
"n_tactics": 76,
"cyclomatic": 4,
"n_automation": 20,
"n_rewrites": 23,
"n_structural": 9,
"automation_only": fal... | 6 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -274,6 +274,23 @@
rw [hcancel, one_mul, mul_comm]]
rw [mul_add, mul_one]
+theorem avoid_double_counting (num den : PNat) :
+ (∑' (x : Bool × ℕ),
+ if x.1 = true → ¬x.2 = 0 then DiscreteLaplaceSampleLoop num den x else 0)
+ = (((2 : ℕ+) : ENNReal))⁻¹ * (1 + ENNReal.ofReal (rexp (-(↑↑den / ↑↑n... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_3 | fde16f766242d313 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "geo_div_geo",
"depth": 1,
"n_commands": 0,
"n_lines": 177,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Geo]\n simp\n\n -- Convert integer division equality into integer inequalities\n have H : (∑' (a : ℕ), if k = a / n th... | [
{
"name": "partial_geometric_series",
"text": "/--\nClosed for for partial geometric series\n-/\nlemma partial_geometric_series {p : ENNReal} (HP2 : p < 1) (B : ℕ) :\n (∑' (a : ℕ), if a < B then p ^ a else 0) = (1 - p ^ B) / (1 - p) := by\n induction B\n · simp\n · rename_i n IH\n have H (a : ℕ) D ... | [
{
"name": "geo_div_geo",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 184,
"n_chars": 4840,
"n_subproofs": 11,
"n_tactics": 161,
"cyclomatic": 7,
"n_automation": 34,
"n_rewrites": 45,
"n_structural": 44,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -454,11 +454,305 @@
· exact trial_one_minus t trial_spec
/--
+Closed for for partial geometric series
+-/
+lemma partial_geometric_series {p : ENNReal} (HP2 : p < 1) (B : ℕ) :
+ (∑' (a : ℕ), if a < B then p ^ a else 0) = (1 - p ^ B) / (1 - p) := by
+ induction B
+ · simp
+ · rename_i n IH
+ have H (a ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_4 | b9c6467df466a08d | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "DiscreteLaplaceSampleLoopIn1_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 55,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [DiscreteLaplaceSampleLoopIn1_apply_pre, DiscreteLaplaceSampleLoopIn1Aux_apply_true]\n simp only [s... | [
{
"name": "DiscreteLaplaceSampleLoopIn1_apply_pre",
"text": "theorem DiscreteLaplaceSampleLoopIn1_apply_pre (t : PNat) (n : ℕ) :\n (DiscreteLaplaceSampleLoopIn1 t) n =\n DiscreteLaplaceSampleLoopIn1Aux t (n, true) *\n (∑' (a : ℕ), DiscreteLaplaceSampleLoopIn1Aux t (a, true))⁻¹ := by\n simp o... | [
{
"name": "DiscreteLaplaceSampleLoop_equiv",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 9,
"n_lines": 268,
"n_chars": 7871,
"n_subproofs": 12,
"n_tactics": 240,
"cyclomatic": 18,
"n_automation": 44,
"n_rewrites": 64,
"n_structural": 65,
"automation_only... | 6 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -81,10 +81,78 @@
· intro x hx
simp [Ne.symm hx]
+theorem DiscreteLaplaceSampleLoopIn1_apply_pre (t : PNat) (n : ℕ) :
+ (DiscreteLaplaceSampleLoopIn1 t) n =
+ DiscreteLaplaceSampleLoopIn1Aux t (n, true) *
+ (∑' (a : ℕ), DiscreteLaplaceSampleLoopIn1Aux t (a, true))⁻¹ := by
+ simp only [Discre... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_5 | 29f701411bf9a833 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "DiscreteLaplaceSampleLoop_equiv",
"depth": 1,
"n_commands": 0,
"n_lines": 262,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply SLang.ext\n intro ⟨ b, n ⟩\n simp [DiscreteLaplaceSampleLoop_apply]\n simp only [DiscreteLaplace... | [
{
"name": "DiscreteLaplaceSampleLoopIn1_apply",
"text": "theorem DiscreteLaplaceSampleLoopIn1_apply (t : PNat) (n : ℕ) (support : n < t) :\n (DiscreteLaplaceSampleLoopIn1 t) n =\n ENNReal.ofReal ((rexp (-ENNReal.toReal (n / t))) *\n ((1 - rexp (- 1 / t)) / (1 - rexp (- 1)))) := by\n rw [Disc... | [
{
"name": "DiscreteLaplaceSampleOptimized_normalizes",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 13,
"n_lines": 10,
"n_chars": 287,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_on... | 9 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -95,6 +95,65 @@
simp [Ne.symm hx])]
simp
+theorem DiscreteLaplaceSampleLoopIn1_apply (t : PNat) (n : ℕ) (support : n < t) :
+ (DiscreteLaplaceSampleLoopIn1 t) n =
+ ENNReal.ofReal ((rexp (-ENNReal.toReal (n / t))) *
+ ((1 - rexp (- 1 / t)) / (1 - rexp (- 1)))) := by
+ rw [DiscreteLaplaceSam... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_6 | 65e94c3fbe27c7c0 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 2 | [
{
"theorem_name": "DiscreteLaplaceSampleOptimized_normalizes",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [<- DiscreteLaplaceSample_equiv]\n apply DiscreteLaplaceSample_normalizes",
"n_chars": 82... | [
{
"name": "DiscreteLaplaceSample_normalizes",
"text": "/--\n``SLang`` Laplace sampler is a proper distribution.\n-/\n@[simp]\ntheorem DiscreteLaplaceSample_normalizes (num den : PNat) :\n ∑' x : ℤ, (DiscreteLaplaceSample num den) x = 1 := by\n have hloop_norm := DiscreteLaplaceSampleLoop_normalizes num ... | [
{
"name": "DiscreteLaplaceSampleMixed_normalizes",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 14,
"n_lines": 13,
"n_chars": 417,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only":... | 10 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -395,6 +395,46 @@
exact hfinish n
/--
+``SLang`` Laplace sampler is a proper distribution.
+-/
+@[simp]
+theorem DiscreteLaplaceSample_normalizes (num den : PNat) :
+ ∑' x : ℤ, (DiscreteLaplaceSample num den) x = 1 := by
+ have hloop_norm := DiscreteLaplaceSampleLoop_normalizes num den
+ simp only [Disc... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_7 | 85387a1e1d253e15 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "DiscreteLaplaceSample_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 69,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hA : 0 ≤ rexp (-(↑↑den / ↑↑num)) := exp_nonneg _\n have hB : 0 ≤ rexp (↑↑den / ↑↑num) := exp_nonneg _\n ... | [
{
"name": "laplace_normalizer_swap",
"text": "theorem laplace_normalizer_swap (num den : ℕ+) :\n (1 - rexp (-(↑↑den / ↑↑num))) * (1 + rexp (-(↑↑den / ↑↑num)))⁻¹ =\n (rexp (↑↑den / ↑↑num) - 1) * (rexp (↑↑den / ↑↑num) + 1)⁻¹ := by\n have hA : rexp (↑↑den / ↑↑num) + 1 ≠ 0 :=\n (Right.add_pos_of_non... | [
{
"name": "DiscreteLaplaceSampleMixed_apply",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 23,
"n_lines": 13,
"n_chars": 586,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": fals... | 16 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -291,6 +291,18 @@
rw [tsum_shift'_1]
exact avoid_double_counting_algebra _ _ hr_ne_one hr_ne_top
+theorem laplace_normalizer_swap (num den : ℕ+) :
+ (1 - rexp (-(↑↑den / ↑↑num))) * (1 + rexp (-(↑↑den / ↑↑num)))⁻¹ =
+ (rexp (↑↑den / ↑↑num) - 1) * (rexp (↑↑den / ↑↑num) + 1)⁻¹ := by
+ have hA : rexp (↑... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_79a8108a6e98_8 | fab5d6c06977cc64 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Laplace/Properties.lean | Properties | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "DiscreteLaplaceSampleLoop_equiv",
"depth": 1,
"n_commands": 0,
"n_lines": 262,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply SLang.ext\n intro ⟨ b, n ⟩\n simp [DiscreteLaplaceSampleLoop_apply]\n simp only [DiscreteLaplace... | [
{
"name": "DiscreteLaplaceSampleLoopIn1_apply",
"text": "theorem DiscreteLaplaceSampleLoopIn1_apply (t : PNat) (n : ℕ) (support : n < t) :\n (DiscreteLaplaceSampleLoopIn1 t) n =\n ENNReal.ofReal ((rexp (-ENNReal.toReal (n / t))) *\n ((1 - rexp (- 1 / t)) / (1 - rexp (- 1)))) := by\n rw [Disc... | [
{
"name": "DiscreteLaplaceSampleMixed_equiv",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 13,
"n_chars": 350,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": fals... | 8 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Util
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic... | @@ -95,6 +95,65 @@
simp [Ne.symm hx])]
simp
+theorem DiscreteLaplaceSampleLoopIn1_apply (t : PNat) (n : ℕ) (support : n < t) :
+ (DiscreteLaplaceSampleLoopIn1 t) n =
+ ENNReal.ofReal ((rexp (-ENNReal.toReal (n / t))) *
+ ((1 - rexp (- 1 / t)) / (1 - rexp (- 1)))) := by
+ rw [DiscreteLaplaceSam... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_138565811916_0 | b7203b2efa215a82 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/UnboundedMax/Privacy.lean | Privacy | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "privUnboundedMax_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices H : (privUnboundedMax ε₁ ε₂) = (sv9_aboveThresh_SPMF exactDiffSum 0 lucky_guess ε₁ ε₂) by\n rw [H]\n ap... | [
{
"name": "exactDiffSum_sens",
"text": "lemma exactDiffSum_sens i : sensitivity (exactDiffSum i) 1 := by\n intro l₁ l₂ H\n cases H\n · rename_i A B C H1 H2\n rw [H1, H2]\n repeat rw [exactDiffSum_append]\n simp [exactDiffSum, exactClippedSum]\n apply Int.le_of_ofNat_le_ofNat\n simp\n ca... | [
{
"name": "privUnboundedMax_DP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 585,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 6,
"n_structural": 5,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Unbo... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Unbo... | @@ -18,12 +18,48 @@
variable (ε₁ ε₂ : ℕ+)
+lemma exactDiffSum_sens i : sensitivity (exactDiffSum i) 1 := by
+ intro l₁ l₂ H
+ cases H
+ · rename_i A B C H1 H2
+ rw [H1, H2]
+ repeat rw [exactDiffSum_append]
+ simp [exactDiffSum, exactClippedSum]
+ apply Int.le_of_ofNat_le_ofNat
+ simp
+ cases ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b79480d08053_0 | 09d09407ab40b8a7 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Mechanism/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "privNoisedQuery_zCDP",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [zCDP]\n apply And.intro\n · exact privNoisedQuery_AC query Δ ε₁ ε₂\n · apply privNoisedQuery_zCDPBound\n... | [
{
"name": "privNoisedQuery_zCDPBound",
"text": "/--\nThe zCDP mechanism with bounded sensitivity satisfies the bound for ``(Δε₂/ε₁)^2``-zCDP.\n-/\ntheorem privNoisedQuery_zCDPBound (query : List T → ℤ) (Δ ε₁ ε₂ : ℕ+) (bounded_sensitivity : sensitivity query Δ) :\n zCDPBound (privNoisedQuery query Δ ε₁ ε₂) ... | [
{
"name": "privNoisedQuery_zCDP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 431,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
import SampCert.DifferentialPrivacy.ZeroConcentrated.Mechanism.Code
/-!
# ``privNo... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
import SampCert.DifferentialPrivacy.ZeroConcentrated.Mechanism.Code
/-!
# ``privNo... | @@ -19,6 +19,83 @@
namespace SLang
/--
+The zCDP mechanism with bounded sensitivity satisfies the bound for ``(Δε₂/ε₁)^2``-zCDP.
+-/
+theorem privNoisedQuery_zCDPBound (query : List T → ℤ) (Δ ε₁ ε₂ : ℕ+) (bounded_sensitivity : sensitivity query Δ) :
+ zCDPBound (privNoisedQuery query Δ ε₁ ε₂) ((1/2) * ((ε₁ : NNRea... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8337676899f4_0 | a575305c02c354e7 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Foundations/While.lean | While | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "probWhile_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro H\n unfold probWhile\n apply iSup_eq_of_tendsto\n · apply probWhileCut_monotonic\n · apply H",
"n_chars": 106... | [
{
"name": "probWhileCut_monotonic",
"text": "/--\nThe ``probWhile`` program is monotonic in terms of the number of unrollings.\n-/\ntheorem probWhileCut_monotonic (cond : T → Bool) (body : T → SLang T) (init : T) (x : T) :\n Monotone (fun n : Nat => probWhileCut cond body n init x) := by\n apply monotone_... | [
{
"name": "probWhile_apply",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 431,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.Foundations.Monad
import SampCert.Foundations.Auto
import Mathlib.Probability.ProbabilityMassFunction... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.Foundations.Monad
import SampCert.Foundations.Auto
import Mathlib.Probability.ProbabilityMassFunction... | @@ -21,6 +21,31 @@
variable {T}
/--
+The ``probWhile`` program is monotonic in terms of the number of unrollings.
+-/
+theorem probWhileCut_monotonic (cond : T → Bool) (body : T → SLang T) (init : T) (x : T) :
+ Monotone (fun n : Nat => probWhileCut cond body n init x) := by
+ apply monotone_nat_of_le_succ
+ int... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_0c2aef1520be_0 | 3c1d4ed708474787 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/GaussPeriodicity.lean | GaussPeriodicity | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "shifted_gauss_summable_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv =>\n arg 1\n intro n\n rw [shifted_gauss_mean_pos μ σ n k]\n apply gauss_convergence_nat_pos h",
... | [
{
"name": "shifted_gauss_mean_pos",
"text": "/--\nShifting ``gauss_term_ℝ`` is equivalent to shifting its mean.\n-/\ntheorem shifted_gauss_mean_pos (μ σ : ℝ) (n : ℤ) (k : ℤ) :\n (gauss_term_ℝ σ μ) (((n + k) : ℤ) : ℝ) = (gauss_term_ℝ σ (μ - k)) n := by\n simp [gauss_term_ℝ, gauss_term_ℝ]\n ring_nf\n\n",
... | [
{
"name": "shifted_gauss_summable_pos",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 323,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | @@ -13,9 +13,22 @@
-/
/--
+Shifting ``gauss_term_ℝ`` is equivalent to shifting its mean.
+-/
+theorem shifted_gauss_mean_pos (μ σ : ℝ) (n : ℤ) (k : ℤ) :
+ (gauss_term_ℝ σ μ) (((n + k) : ℤ) : ℝ) = (gauss_term_ℝ σ (μ - k)) n := by
+ simp [gauss_term_ℝ, gauss_term_ℝ]
+ ring_nf
+
+/--
``gauss_term_ℝ`` is summable u... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_0c2aef1520be_1 | b169148f193edc6f | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/GaussPeriodicity.lean | GaussPeriodicity | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "shifted_gauss_summable_neg",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv =>\n arg 1\n intro n\n rw [shifted_gauss_mean_neg μ n k]\n apply gauss_convergence_nat_pos h",
... | [
{
"name": "shifted_gauss_mean_neg",
"text": "/--\nShifting ``gauss_term_ℝ`` is equivalent to shifting its mean.\n-/\ntheorem shifted_gauss_mean_neg (μ : ℝ) (n : ℤ) (k : ℤ) :\n (gauss_term_ℝ σ μ) (((-(n + k)) : ℤ) : ℝ) = (gauss_term_ℝ σ (-(μ + k))) n := by\n simp [gauss_term_ℝ, gauss_term_ℝ]\n ring_nf\n\n... | [
{
"name": "shifted_gauss_summable_neg",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 323,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | @@ -13,9 +13,22 @@
-/
/--
+Shifting ``gauss_term_ℝ`` is equivalent to shifting its mean.
+-/
+theorem shifted_gauss_mean_neg (μ : ℝ) (n : ℤ) (k : ℤ) :
+ (gauss_term_ℝ σ μ) (((-(n + k)) : ℤ) : ℝ) = (gauss_term_ℝ σ (-(μ + k))) n := by
+ simp [gauss_term_ℝ, gauss_term_ℝ]
+ ring_nf
+
+/--
``gauss_term_ℝ`` is summab... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
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