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_eb9bd13f8383_1 | 9995ab57d7eef01a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/TraceEq.lean | TraceEq | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 3 | [
{
"theorem_name": "mem_traces_singleton_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [mem_traces_iff, MTr.singleton_iff lts s μ]",
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 2,... | [
{
"name": "mem_traces_iff",
"text": "/-- Definition of `LTS.traces` for general label sequences, ... -/\ntheorem mem_traces_iff {lts : LTS State Label} (μs : List Label) :\n μs ∈ lts.traces s ↔ ∃ s', lts.MTr s μs s' := Iff.rfl\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 199,
"n_subproofs": ... | [
{
"name": "mem_traces_cons_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 288,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | @@ -41,9 +41,15 @@
transition labelled by `μs` originating from `s`. -/
def traces (lts : LTS State Label) (s : State) := { μs : List Label | ∃ s', lts.MTr s μs s' }
+/-- Definition of `LTS.traces` for general label sequences, ... -/
+theorem mem_traces_iff {lts : LTS State Label} (μs : List Label) :
+ μs ∈ lts.tr... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_eb9bd13f8383_3 | 28e4a619efde59c3 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/TraceEq.lean | TraceEq | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 3 | [
{
"theorem_name": "mem_traces_singleton_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [mem_traces_iff, MTr.singleton_iff lts s μ]",
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 2,... | [
{
"name": "mem_traces_iff",
"text": "/-- Definition of `LTS.traces` for general label sequences, ... -/\ntheorem mem_traces_iff {lts : LTS State Label} (μs : List Label) :\n μs ∈ lts.traces s ↔ ∃ s', lts.MTr s μs s' := Iff.rfl\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 199,
"n_subproofs": ... | [
{
"name": "TraceEq.exists_mTr_of_mTr",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 366,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | @@ -41,6 +41,10 @@
transition labelled by `μs` originating from `s`. -/
def traces (lts : LTS State Label) (s : State) := { μs : List Label | ∃ s', lts.MTr s μs s' }
+/-- Definition of `LTS.traces` for general label sequences, ... -/
+theorem mem_traces_iff {lts : LTS State Label} (μs : List Label) :
+ μs ∈ lts.tr... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_eb9bd13f8383_4 | 0f40e5c430832b9a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/TraceEq.lean | TraceEq | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "TraceEq.exists_tr_of_tr",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [←mem_traces_singleton_iff, ←h, mem_traces_singleton_iff]\n exact ⟨s₁', htr⟩",
"n_chars": 95,
"n_subpro... | [
{
"name": "mem_traces_singleton_iff",
"text": "/-- ... singleton sequences, ... -/\ntheorem mem_traces_singleton_iff {lts : LTS State Label} (μ : Label) :\n [μ] ∈ lts.traces s ↔ ∃ s', lts.Tr s μ s' := by\n simp_rw [mem_traces_iff, MTr.singleton_iff lts s μ]\n\n",
"fan_in": 1,
"n_lines": 6,
"... | [
{
"name": "TraceEq.exists_tr_of_tr",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 398,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | @@ -45,6 +45,11 @@
theorem mem_traces_iff {lts : LTS State Label} (μs : List Label) :
μs ∈ lts.traces s ↔ ∃ s', lts.MTr s μs s' := Iff.rfl
+/-- ... singleton sequences, ... -/
+theorem mem_traces_singleton_iff {lts : LTS State Label} (μ : Label) :
+ [μ] ∈ lts.traces s ↔ ∃ s', lts.Tr s μ s' := by
+ simp_rw [me... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_eb9bd13f8383_5 | 5d146d2c26f00455 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/TraceEq.lean | TraceEq | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "TraceEq.traceEq_of_tr_of_tr",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [TraceEq] at h\n simp_rw [TraceEq, Deterministic.traces_of_tr htr₁, Deterministic.traces_of_tr htr₂, h]",
... | [
{
"name": "Deterministic.traces_of_tr",
"text": "/-- In a deterministic lts, a state's traces are determined by any of its predecessors. -/\ntheorem Deterministic.traces_of_tr {lts : LTS State Label} [lts.Deterministic]\n (h : lts.Tr s μ s') : lts.traces s' = {μs | μ :: μs ∈ lts.traces s} := by\n ext μs... | [
{
"name": "TraceEq.traceEq_of_tr_of_tr",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 537,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | @@ -41,6 +41,18 @@
transition labelled by `μs` originating from `s`. -/
def traces (lts : LTS State Label) (s : State) := { μs : List Label | ∃ s', lts.MTr s μs s' }
+/-- In a deterministic lts, a state's traces are determined by any of its predecessors. -/
+theorem Deterministic.traces_of_tr {lts : LTS State Label... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_eb9bd13f8383_6 | 020c2f3621a7374e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/TraceEq.lean | TraceEq | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "Deterministic.traceEq_iff_simulationEquiv",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨fun h =>\n ⟨⟨_, h, Deterministic.isSimulation_traceEq⟩, _, h.symm, Deterministic.isSimulation_tr... | [
{
"name": "SimulationEquiv.traceEq",
"text": "/-- Simulation equivalence implies trace equivalence. -/\ntheorem SimulationEquiv.traceEq (h : s₁ ≤≥[lts₁,lts₂] s₂) : s₁ ~tr[lts₁,lts₂] s₂ := by\n obtain ⟨⟨_, h, hr⟩, _, h', hr'⟩ := h\n exact (hr.traces_subset h).antisymm (hr'.traces_subset h')\n\n",
"fan_... | [
{
"name": "Deterministic.traceEq_iff_simulationEquiv",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 536,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Basic
public import Cslib.Foundations.Semantics.LTS.Simulation
/-!
# Trace Equivalence
Definitions and re... | @@ -129,10 +129,18 @@
obtain ⟨s₂', htr2⟩ := h.exists_tr_of_tr htr1
use s₂', htr2, h.traceEq_of_tr_of_tr htr1 htr2
+/-- Simulation equivalence implies trace equivalence. -/
+theorem SimulationEquiv.traceEq (h : s₁ ≤≥[lts₁,lts₂] s₂) : s₁ ~tr[lts₁,lts₂] s₂ := by
+ obtain ⟨⟨_, h, hr⟩, _, h', hr'⟩ := h
+ exact (hr... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_34b7a6b80311_0 | 91416fc034bd8609 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/RelatesInSteps.lean | RelatesInSteps | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "RelatesInSteps.succ_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · exact RelatesInSteps.succ\n · rintro ⟨t', h_steps, h_red⟩\n exact .tail _ t' b n h_steps h_red... | [
{
"name": "RelatesInSteps.succ",
"text": "lemma RelatesInSteps.succ {n : ℕ} (h : RelatesInSteps r a b (n + 1)) :\n ∃ t', RelatesInSteps r a t' n ∧ r t' b := by\n cases h with\n | tail t' _ _ hsteps hstep => exact ⟨t', hsteps, hstep⟩\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 204,
"n_su... | [
{
"name": "RelatesInSteps.succ_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 261,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 3,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2025 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Cslib.Init
public import Mathlib.Logic.Relation
/-! # Relations Across Steps
This file defines `Relation.RelatesInSteps` (and `Relation.Relates... | /-
Copyright (c) 2025 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Cslib.Init
public import Mathlib.Logic.Relation
/-! # Relations Across Steps
This file defines `Relation.RelatesInSteps` (and `Relation.Relates... | @@ -76,10 +76,15 @@
rw [← Nat.add_assoc]
exact .tail _ t' t'' (n + k) (ih h₁) hstep
+lemma RelatesInSteps.succ {n : ℕ} (h : RelatesInSteps r a b (n + 1)) :
+ ∃ t', RelatesInSteps r a t' n ∧ r t' b := by
+ cases h with
+ | tail t' _ _ hsteps hstep => exact ⟨t', hsteps, hstep⟩
+
lemma RelatesInSteps.suc... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_34b7a6b80311_1 | 440dc8e0a064a43e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/RelatesInSteps.lean | RelatesInSteps | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "RelatesWithinSteps.refl",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n RelatesWithinSteps.of_relatesInSteps (RelatesInSteps.refl a)",
"n_chars": 63,
"n_subproofs": 0,
"n_tactics... | [
{
"name": "RelatesWithinSteps.of_relatesInSteps",
"text": "/-- `RelatesInSteps` implies `RelatesWithinSteps` with the same bound. -/\nlemma RelatesWithinSteps.of_relatesInSteps {a b : α} {n : ℕ} (h : RelatesInSteps r a b n) :\n RelatesWithinSteps r a b n :=\n ⟨n, Nat.le_refl n, h⟩\n\n",
"fan_in": 2,... | [
{
"name": "RelatesWithinSteps.refl",
"fan_in": 11,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 135,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2025 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Cslib.Init
public import Mathlib.Logic.Relation
/-! # Relations Across Steps
This file defines `Relation.RelatesInSteps` (and `Relation.Relates... | /-
Copyright (c) 2025 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Cslib.Init
public import Mathlib.Logic.Relation
/-! # Relations Across Steps
This file defines `Relation.RelatesInSteps` (and `Relation.Relates... | @@ -83,10 +83,17 @@
def RelatesWithinSteps (r : α → α → Prop) (a b : α) (n : ℕ) : Prop :=
∃ m ≤ n, RelatesInSteps r a b m
-lemma RelatesWithinSteps.refl (a : α) : RelatesWithinSteps r a a 0 := sorry
+/-- `RelatesInSteps` implies `RelatesWithinSteps` with the same bound. -/
+lemma RelatesWithinSteps.of_relatesInSt... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_5f24eef397a9_0 | bd1617408585129f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Simulation.lean | Simulation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "Similarity.trans",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨r1, hr1, hr1s⟩ := h1\n obtain ⟨r2, hr2, hr2s⟩ := h2\n use! Relation.Comp r1 r2, s2, hr1, hr2, IsSimulation.comp ... | [
{
"name": "IsSimulation.comp",
"text": "/-- The composition of two simulations is a simulation. -/\ntheorem IsSimulation.comp\n (r1 : State₁ → State₂ → Prop)\n (r2 : State₂ → State₃ → Prop)\n (h1 : IsSimulation lts₁ lts₂ r1) (h2 : IsSimulation lts₂ lts₃ r2) :\n IsSimulation lts₁ lts₃ (Relation.C... | [
{
"name": "Similarity.trans",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 314,
"n_subproofs": 2,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.HasTau
/-! # IsSimulation and Similarity
A simulation is a binary relation on the states of two `LTS`s: i... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.HasTau
/-! # IsSimulation and Similarity
A simulation is a binary relation on the states of two `LTS`s: i... | @@ -78,9 +78,24 @@
/-- Notation for homogeneous similarity. -/
scoped notation s:max " ≤[" lts "] " s':max => HomSimilarity lts s s'
+/-- The composition of two simulations is a simulation. -/
+theorem IsSimulation.comp
+ (r1 : State₁ → State₂ → Prop)
+ (r2 : State₂ → State₃ → Prop)
+ (h1 : IsSimulation lt... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_5f24eef397a9_2 | c672dfffafeec51d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Simulation.lean | Simulation | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "IsSimulation.isSimulation_saturate_left",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro s₁ s₂ hr μ s₁' h\n cases h\n case refl =>\n use s₂, .refl, hr\n case tr sb sb' hstr1 h... | [
{
"name": "IsSimulation.follow_internal",
"text": "/-- Utility theorem for following internal transitions along a saturated lts. -/\nlemma IsSimulation.follow_internal [HasTau Label] {lts₁ : LTS State₁ Label}\n {lts₂ : LTS State₂ Label} (h : IsSimulation lts₁ lts₂.saturate r) (hr : r s₁ s₂)\n (hstr : ... | [
{
"name": "IsSimulation.isSimulation_saturate_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 759,
"n_subproofs": 3,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 7,
"automation_only... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.HasTau
/-! # IsSimulation and Similarity
A simulation is a binary relation on the states of two `LTS`s: i... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.HasTau
/-! # IsSimulation and Similarity
A simulation is a binary relation on the states of two `LTS`s: i... | @@ -137,10 +137,32 @@
(SimulationEquiv lts₁ lts₃) where
trans := SimulationEquiv.trans
+/-- Utility theorem for following internal transitions along a saturated lts. -/
+lemma IsSimulation.follow_internal [HasTau Label] {lts₁ : LTS State₁ Label}
+ {lts₂ : LTS State₂ Label} (h : IsSimulation lts₁ lts₂.satur... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ae3d472c2cc6_0 | 59908302feb63215 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/HasTau.lean | HasTau | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 4 | [
{
"theorem_name": "tr_le_tr_saturate",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n fun _ _ _ => STr.single",
"n_chars": 26,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "STr.single",
"text": "/-- Any transition is also a saturated transition. -/\ntheorem STr.single [HasTau Label] {lts : LTS State Label} :\n lts.Tr s μ s' → lts.STr s μ s' := by\n intro h\n apply STr.tr .refl h .refl\n\n",
"fan_in": 4,
"n_lines": 7,
"n_chars": 199,
"n_subproofs... | [
{
"name": "tr_le_tr_saturate",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 122,
"n_subproofs": 0,
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"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | @@ -50,8 +50,15 @@
theorem saturate_tr_sTr [HasTau Label] {lts : LTS State Label} :
lts.saturate.Tr = lts.STr := by rfl
-lemma tr_le_tr_saturate [HasTau Label] (lts : LTS State Label) : lts.Tr ≤ lts.saturate.Tr := sorry
+/-- Any transition is also a saturated transition. -/
+theorem STr.single [HasTau Label] {lts... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ae3d472c2cc6_1 | 68aa842f35b84b85 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/HasTau.lean | HasTau | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 5 | [
{
"theorem_name": "saturate_τsTr_τSTr_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext s s'\n apply Iff.intro <;> intro h\n case mp =>\n induction h\n case refl => constructor\n case tail... | [
{
"name": "sTr_τSTr_iff",
"text": "/-- STr transitions labeled by HasTau.τ are exactly the τSTr transitions. -/\ntheorem sTr_τSTr_iff [HasTau Label] (lts : LTS State Label) :\n lts.STr s HasTau.τ s' ↔ lts.τSTr s s' := by\n apply Iff.intro <;> intro h\n case mp =>\n cases h\n case refl => exact .r... | [
{
"name": "saturate_τsTr_τSTr_iff",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 590,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 6,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | @@ -56,16 +56,45 @@
intro h
apply STr.tr .refl h .refl
+/-- STr transitions labeled by HasTau.τ are exactly the τSTr transitions. -/
+theorem sTr_τSTr_iff [HasTau Label] (lts : LTS State Label) :
+ lts.STr s HasTau.τ s' ↔ lts.τSTr s s' := by
+ apply Iff.intro <;> intro h
+ case mp =>
+ cases h
+ case... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ae3d472c2cc6_2 | 763903cf02c068dc | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/HasTau.lean | HasTau | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 5 | [
{
"theorem_name": "saturate_τsTr_τSTr_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext s s'\n apply Iff.intro <;> intro h\n case mp =>\n induction h\n case refl => constructor\n case tail... | [
{
"name": "sTr_τSTr_iff",
"text": "/-- STr transitions labeled by HasTau.τ are exactly the τSTr transitions. -/\ntheorem sTr_τSTr_iff [HasTau Label] (lts : LTS State Label) :\n lts.STr s HasTau.τ s' ↔ lts.τSTr s s' := by\n apply Iff.intro <;> intro h\n case mp =>\n cases h\n case refl => exact .r... | [
{
"name": "STr.trans_τ",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 343,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | @@ -56,12 +56,29 @@
intro h
apply STr.tr .refl h .refl
+/-- STr transitions labeled by HasTau.τ are exactly the τSTr transitions. -/
+theorem sTr_τSTr_iff [HasTau Label] (lts : LTS State Label) :
+ lts.STr s HasTau.τ s' ↔ lts.τSTr s s' := by
+ apply Iff.intro <;> intro h
+ case mp =>
+ cases h
+ case... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ae3d472c2cc6_3 | f6b7783e77844220 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/HasTau.lean | HasTau | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 4 | [
{
"theorem_name": "tr_le_tr_saturate",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n fun _ _ _ => STr.single",
"n_chars": 26,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "STr.single",
"text": "/-- Any transition is also a saturated transition. -/\ntheorem STr.single [HasTau Label] {lts : LTS State Label} :\n lts.Tr s μ s' → lts.STr s μ s' := by\n intro h\n apply STr.tr .refl h .refl\n\n",
"fan_in": 4,
"n_lines": 7,
"n_chars": 199,
"n_subproofs... | [
{
"name": "saturate_tr_saturate_sTr",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 20,
"n_chars": 662,
"n_subproofs": 0,
"n_tactics": 17,
"cyclomatic": 6,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 10,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | @@ -50,6 +50,12 @@
theorem saturate_tr_sTr [HasTau Label] {lts : LTS State Label} :
lts.saturate.Tr = lts.STr := by rfl
+/-- Any transition is also a saturated transition. -/
+theorem STr.single [HasTau Label] {lts : LTS State Label} :
+ lts.Tr s μ s' → lts.STr s μ s' := by
+ intro h
+ apply STr.tr .refl h .... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ae3d472c2cc6_4 | ae882431515ea94e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/HasTau.lean | HasTau | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 4 | [
{
"theorem_name": "tr_le_tr_saturate",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n fun _ _ _ => STr.single",
"n_chars": 26,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "STr.single",
"text": "/-- Any transition is also a saturated transition. -/\ntheorem STr.single [HasTau Label] {lts : LTS State Label} :\n lts.Tr s μ s' → lts.STr s μ s' := by\n intro h\n apply STr.tr .refl h .refl\n\n",
"fan_in": 4,
"n_lines": 7,
"n_chars": 199,
"n_subproofs... | [
{
"name": "SMTr.fromMTr",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 387,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Foundations.Semantics.LTS.Relation
/-!
# LTS with a special "internal" transition `τ`.
-/
@[expose] public section
namespace Cslib... | @@ -50,6 +50,12 @@
theorem saturate_tr_sTr [HasTau Label] {lts : LTS State Label} :
lts.saturate.Tr = lts.STr := by rfl
+/-- Any transition is also a saturated transition. -/
+theorem STr.single [HasTau Label] {lts : LTS State Label} :
+ lts.Tr s μ s' → lts.STr s μ s' := by
+ intro h
+ apply STr.tr .refl h .... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_3fa66cf42b28_0 | db4fa06c31939684 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/SecretSharing/Shamir/Polynomial.lean | Polynomial | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "constantCoeff_sharingPolynomial",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [_root_.Polynomial.constantCoeff_apply] using\n coeff_zero_sharingPolynomial secretValue tail",
... | [
{
"name": "coeff_zero_sharingPolynomial",
"text": "theorem coeff_zero_sharingPolynomial (secretValue : F) (tail : _root_.Polynomial F) :\n (sharingPolynomial secretValue tail).coeff 0 = secretValue := by\n simp [sharingPolynomial]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 183,
"n_subpr... | [
{
"name": "constantCoeff_sharingPolynomial",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 269,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 1 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | @@ -44,8 +44,14 @@
(sharingPolynomial secretValue tail).eval x = secretValue + x * tail.eval x := by
simp [sharingPolynomial, mul_comm]
+theorem coeff_zero_sharingPolynomial (secretValue : F) (tail : _root_.Polynomial F) :
+ (sharingPolynomial secretValue tail).coeff 0 = secretValue := by
+ simp [sharingP... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_3fa66cf42b28_1 | 2e21593c17c836e3 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/SecretSharing/Shamir/Polynomial.lean | Polynomial | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "degree_sharingPolynomial_lt_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hsharing : sharingPolynomial secretValue tail = 0\n · simp [hsharing]\n · rw [_root_.Polynomial... | [
{
"name": "natDegree_sharingPolynomial_le",
"text": "/-- If the tail polynomial has degree `< n`, then the sharing polynomial has\nnatural degree at most `n`. -/\ntheorem natDegree_sharingPolynomial_le (secretValue : F) (tail : _root_.Polynomial F) {n : ℕ}\n (hdeg : tail.degree < n) :\n (sharingPolyno... | [
{
"name": "degree_sharingPolynomial_lt_succ",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 537,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false... | 1 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | @@ -45,13 +45,34 @@
simp [sharingPolynomial, mul_comm]
/-- If the tail polynomial has degree `< n`, then the sharing polynomial has
+natural degree at most `n`. -/
+theorem natDegree_sharingPolynomial_le (secretValue : F) (tail : _root_.Polynomial F) {n : ℕ}
+ (hdeg : tail.degree < n) :
+ (sharingPolynomial... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_3fa66cf42b28_2 | e4f410332c3ec89d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/SecretSharing/Shamir/Polynomial.lean | Polynomial | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "degree_sharingPolynomial_lt_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hsharing : sharingPolynomial secretValue tail = 0\n · simp [hsharing]\n · rw [_root_.Polynomial... | [
{
"name": "natDegree_sharingPolynomial_le",
"text": "/-- If the tail polynomial has degree `< n`, then the sharing polynomial has\nnatural degree at most `n`. -/\ntheorem natDegree_sharingPolynomial_le (secretValue : F) (tail : _root_.Polynomial F) {n : ℕ}\n (hdeg : tail.degree < n) :\n (sharingPolyno... | [
{
"name": "degree_sharingPolynomial_tailPolynomial_lt_succ",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 406,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automatio... | 3 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | @@ -52,13 +52,34 @@
simp [sharingPolynomial, mul_comm]
/-- If the tail polynomial has degree `< n`, then the sharing polynomial has
+natural degree at most `n`. -/
+theorem natDegree_sharingPolynomial_le (secretValue : F) (tail : _root_.Polynomial F) {n : ℕ}
+ (hdeg : tail.degree < n) :
+ (sharingPolynomial... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_3fa66cf42b28_3 | ad2fa225ca3cd4cc | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/SecretSharing/Shamir/Polynomial.lean | Polynomial | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "reconstruct_sharingPolynomial_eq_secret",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [reconstruct_eq_constantCoeff_of_eval_eq\n (p := sharingPolynomial secretValue tail) hx hdeg]... | [
{
"name": "constantCoeff_sharingPolynomial",
"text": "theorem constantCoeff_sharingPolynomial (secretValue : F) (tail : _root_.Polynomial F) :\n (sharingPolynomial secretValue tail).constantCoeff = secretValue := by\n simpa [_root_.Polynomial.constantCoeff_apply] using\n coeff_zero_sharingPolynomial ... | [
{
"name": "reconstruct_sharingPolynomial_eq_secret",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 605,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only"... | 3 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Init
public import Mathlib.LinearAlgebra.Lagrange
/-!
# Shamir Secret Sharing: Polynomial Utilities
This file contains the Sham... | @@ -48,6 +48,11 @@
(sharingPolynomial secretValue tail).coeff 0 = secretValue := by
simp [sharingPolynomial]
+theorem constantCoeff_sharingPolynomial (secretValue : F) (tail : _root_.Polynomial F) :
+ (sharingPolynomial secretValue tail).constantCoeff = secretValue := by
+ simpa [_root_.Polynomial.constan... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_0 | edc2985fb366699b | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "cons_injective_left",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n cons_injective2.left _",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automati... | [
{
"name": "cons_injective2",
"text": "theorem cons_injective2 : Function.Injective2 (cons : α → ωSequence α → ωSequence α) :=\nfun x y s t h =>\n ⟨by rw [← get_zero_cons x s, h, get_zero_cons],\n ωSequence.ext fun n => by rw [← get_succ_cons n s x, h, get_succ_cons]⟩\n\n",
"fan_in": 2,
"n_lines"... | [
{
"name": "cons_injective_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 4,
"n_chars": 116,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -98,8 +98,14 @@
theorem drop_succ (n : ℕ) (s : ωSequence α) : drop (succ n) s = drop n (tail s) :=
rfl
-theorem cons_injective_left (s : ωSequence α) : Function.Injective fun x => cons x s := sorry
+theorem cons_injective2 : Function.Injective2 (cons : α → ωSequence α → ωSequence α) :=
+fun x y s t h =>
+ ⟨by... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_1 | 8129198522bca3f5 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "cons_injective_left",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n cons_injective2.left _",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automati... | [
{
"name": "cons_injective2",
"text": "theorem cons_injective2 : Function.Injective2 (cons : α → ωSequence α → ωSequence α) :=\nfun x y s t h =>\n ⟨by rw [← get_zero_cons x s, h, get_zero_cons],\n ωSequence.ext fun n => by rw [← get_succ_cons n s x, h, get_succ_cons]⟩\n\n",
"fan_in": 2,
"n_lines"... | [
{
"name": "cons_injective_right",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 4,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -98,8 +98,14 @@
theorem drop_succ (n : ℕ) (s : ωSequence α) : drop (succ n) s = drop n (tail s) :=
rfl
-theorem cons_injective_right (x : α) : Function.Injective (cons x) := sorry
+theorem cons_injective2 : Function.Injective2 (cons : α → ωSequence α → ωSequence α) :=
+fun x y s t h =>
+ ⟨by rw [← get_zero_co... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_2 | a084d1f6f6a259b4 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "map_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← ωSequence.eta (map f s), tail_map, head_map]",
"n_chars": 59,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": ... | [
{
"name": "tail_map",
"text": "theorem tail_map (s : ωSequence α) : tail (map f s) = map f (tail s) := 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,
"automa... | [
{
"name": "map_eq",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 4,
"n_chars": 141,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
}
... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -106,11 +106,14 @@
theorem get_map (n : ℕ) (s : ωSequence α) : (map f s) n = f (s n) :=
rfl
+theorem tail_map (s : ωSequence α) : tail (map f s) = map f (tail s) := rfl
+
@[simp, scoped grind =]
theorem head_map (s : ωSequence α) : head (map f s) = f (head s) :=
rfl
-theorem map_eq (s : ωSequence α) : m... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_3 | 49562b0323a05563 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "tail_const",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n suffices tail (a ::ω const a) = const a by rwa [← const_eq] at this\n rfl",
"n_chars": 79,
"n_subproofs": 1,
"n_tactic... | [
{
"name": "const_eq",
"text": "theorem const_eq (a : α) : const a = a ::ω const a := by\n apply ωSequence.ext; intro n\n cases n <;> rfl\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
... | [
{
"name": "tail_const",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 162,
"n_subproofs": 1,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -143,8 +143,14 @@
end Zip
+theorem const_eq (a : α) : const a = a ::ω const a := by
+ apply ωSequence.ext; intro n
+ cases n <;> rfl
+
@[simp, scoped grind =]
-theorem tail_const (a : α) : tail (const a) = const a := sorry
+theorem tail_const (a : α) : tail (const a) = const a :=
+ suffices tail (a ::ω cons... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_4 | ede9ef17baeb76a2 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "get_succ_iterate'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [get_iterate, succ_eq_add_one, add_comm, Function.iterate_add_apply]\n rfl",
"n_chars": 83,
"n_subproofs": 0,... | [
{
"name": "get_iterate",
"text": "theorem get_iterate (f : α → α) (a : α) (n : ℕ) :\n iterate f a n = f^[n] a :=\n rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 95,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural"... | [
{
"name": "get_succ_iterate'",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 195,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -168,15 +168,22 @@
theorem head_iterate (f : α → α) (a : α) : head (iterate f a) = a :=
rfl
+theorem get_iterate (f : α → α) (a : α) (n : ℕ) :
+ iterate f a n = f^[n] a :=
+ rfl
+
theorem get_succ_iterate' (n : ℕ) (f : α → α) (a : α) :
- iterate f a (succ n) = f (iterate f a n) := sorry
+ iterate f ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_5 | c63e4db565a97e6f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "get_succ_iterate'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [get_iterate, succ_eq_add_one, add_comm, Function.iterate_add_apply]\n rfl",
"n_chars": 83,
"n_subproofs": 0,... | [
{
"name": "get_iterate",
"text": "theorem get_iterate (f : α → α) (a : α) (n : ℕ) :\n iterate f a n = f^[n] a :=\n rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 95,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural"... | [
{
"name": "tail_iterate",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 214,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nesting": ... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -168,8 +168,14 @@
theorem head_iterate (f : α → α) (a : α) : head (iterate f a) = a :=
rfl
+theorem get_iterate (f : α → α) (a : α) (n : ℕ) :
+ iterate f a n = f^[n] a :=
+ rfl
+
theorem get_succ_iterate' (n : ℕ) (f : α → α) (a : α) :
- iterate f a (succ n) = f (iterate f a n) := sorry
+ iterate f a... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_6 | e9fd6acbae6de8fb | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "get_succ_iterate'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [get_iterate, succ_eq_add_one, add_comm, Function.iterate_add_apply]\n rfl",
"n_chars": 83,
"n_subproofs": 0,... | [
{
"name": "get_iterate",
"text": "theorem get_iterate (f : α → α) (a : α) (n : ℕ) :\n iterate f a n = f^[n] a :=\n rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 95,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural"... | [
{
"name": "iterate_eq",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 5,
"n_chars": 155,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -168,8 +168,14 @@
theorem head_iterate (f : α → α) (a : α) : head (iterate f a) = a :=
rfl
+theorem get_iterate (f : α → α) (a : α) (n : ℕ) :
+ iterate f a n = f^[n] a :=
+ rfl
+
theorem get_succ_iterate' (n : ℕ) (f : α → α) (a : α) :
- iterate f a (succ n) = f (iterate f a n) := sorry
+ iterate f a... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_7 | 0eb1dee6208a4c6a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "get_succ_iterate'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [get_iterate, succ_eq_add_one, add_comm, Function.iterate_add_apply]\n rfl",
"n_chars": 83,
"n_subproofs": 0,... | [
{
"name": "get_iterate",
"text": "theorem get_iterate (f : α → α) (a : α) (n : ℕ) :\n iterate f a n = f^[n] a :=\n rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 95,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural"... | [
{
"name": "get_succ_iterate",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -168,8 +168,14 @@
theorem head_iterate (f : α → α) (a : α) : head (iterate f a) = a :=
rfl
+theorem get_iterate (f : α → α) (a : α) (n : ℕ) :
+ iterate f a n = f^[n] a :=
+ rfl
+
theorem get_succ_iterate' (n : ℕ) (f : α → α) (a : α) :
- iterate f a (succ n) = f (iterate f a n) := sorry
+ iterate f a... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_8 | 622ab4635f81b100 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "get_succ_iterate'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [get_iterate, succ_eq_add_one, add_comm, Function.iterate_add_apply]\n rfl",
"n_chars": 83,
"n_subproofs": 0,... | [
{
"name": "get_iterate",
"text": "theorem get_iterate (f : α → α) (a : α) (n : ℕ) :\n iterate f a n = f^[n] a :=\n rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 95,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural"... | [
{
"name": "iterate_id",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 112,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -168,12 +168,17 @@
theorem head_iterate (f : α → α) (a : α) : head (iterate f a) = a :=
rfl
+theorem get_iterate (f : α → α) (a : α) (n : ℕ) :
+ iterate f a n = f^[n] a :=
+ rfl
+
@[simp, scoped grind =]
theorem get_zero_iterate (f : α → α) (a : α) : (iterate f a) 0 = a :=
rfl
@[simp, scoped grind ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_9 | 9d19a34cde19b28d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "tail_iterate",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext n\n rw [get_tail]\n induction n with\n | zero => rfl\n | succ n ih => rw [get_succ_iterate', ih, get_succ_iterate']",
... | [
{
"name": "get_succ_iterate'",
"text": "theorem get_succ_iterate' (n : ℕ) (f : α → α) (a : α) :\n iterate f a (succ n) = f (iterate f a n) := by\n rw [get_iterate, succ_eq_add_one, add_comm, Function.iterate_add_apply]\n rfl\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 195,
"n_subproofs"... | [
{
"name": "map_iterate",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 8,
"n_lines": 4,
"n_chars": 155,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2... | 4 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -172,12 +172,17 @@
iterate f a n = f^[n] a :=
rfl
+theorem get_succ_iterate' (n : ℕ) (f : α → α) (a : α) :
+ iterate f a (succ n) = f (iterate f a n) := by
+ rw [get_iterate, succ_eq_add_one, add_comm, Function.iterate_add_apply]
+ rfl
+
theorem tail_iterate (f : α → α) (a : α) : tail (iterate f a) =... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_10 | 0a2c1eb420a72f23 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "append_right_inj",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨append_right_injective x a b, by simp +contextual⟩",
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 1,
"cyclo... | [
{
"name": "append_right_injective",
"text": "lemma append_right_injective (h : x ++ω a = x ++ω b) : a = b := by\n ext n; replace h := congr_arg (fun a ↦ a (x.length + n)) h; simpa using h\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 148,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic"... | [
{
"name": "append_right_inj",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 141,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -210,8 +210,12 @@
@[simp, scoped grind =]
lemma get_append_length : (x ++ω a) x.length = a 0 := get_append_right 0 x a
+lemma append_right_injective (h : x ++ω a = x ++ω b) : a = b := by
+ ext n; replace h := congr_arg (fun a ↦ a (x.length + n)) h; simpa using h
+
@[simp, scoped grind =]
-lemma append_right_in... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_11 | 25d68eb75abb3884 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 4 | [
{
"theorem_name": "append_left_injective",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply List.ext_getElem hl\n intros\n rw [← get_append_left, ← get_append_left, h]",
"n_chars": 91,
"n_subpr... | [
{
"name": "get_append_left",
"text": "lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by\n induction x generalizing n with\n | nil => simp at h\n | cons b x ih =>\n rcases n with (_ | n)\n · simp\n · simp [ih n (by simpa using h), cons_append_ωSequence]\n\n",
"fan_in": 4,
... | [
{
"name": "append_left_injective",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 184,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -195,6 +195,14 @@
| List.cons a l₁, l₂, s => by
rw [List.cons_append, cons_append_ωSequence, cons_append_ωSequence, append_append_ωSequence l₁]
+lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by
+ induction x generalizing n with
+ | nil => simp at h
+ | cons b x ih =>
+ rcases n wit... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_12 | c87fb9cea9734fc9 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 4 | [
{
"theorem_name": "append_left_injective",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply List.ext_getElem hl\n intros\n rw [← get_append_left, ← get_append_left, h]",
"n_chars": 91,
"n_subpr... | [
{
"name": "get_append_left",
"text": "lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by\n induction x generalizing n with\n | nil => simp at h\n | cons b x ih =>\n rcases n with (_ | n)\n · simp\n · simp [ih n (by simpa using h), cons_append_ωSequence]\n\n",
"fan_in": 4,
... | [
{
"name": "append_left_right_injective",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 232,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -195,6 +195,14 @@
| List.cons a l₁, l₂, s => by
rw [List.cons_append, cons_append_ωSequence, cons_append_ωSequence, append_append_ωSequence l₁]
+lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by
+ induction x generalizing n with
+ | nil => simp at h
+ | cons b x ih =>
+ rcases n wit... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_13 | 46c88f7397813680 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 4 | [
{
"theorem_name": "append_left_injective",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply List.ext_getElem hl\n intros\n rw [← get_append_left, ← get_append_left, h]",
"n_chars": 91,
"n_subpr... | [
{
"name": "get_append_left",
"text": "lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by\n induction x generalizing n with\n | nil => simp at h\n | cons b x ih =>\n rcases n with (_ | n)\n · simp\n · simp [ih n (by simpa using h), cons_append_ωSequence]\n\n",
"fan_in": 4,
... | [
{
"name": "take_append_of_le_length",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 8,
"n_lines": 6,
"n_chars": 200,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -195,6 +195,14 @@
| List.cons a l₁, l₂, s => by
rw [List.cons_append, cons_append_ωSequence, cons_append_ωSequence, append_append_ωSequence l₁]
+lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by
+ induction x generalizing n with
+ | nil => simp at h
+ | cons b x ih =>
+ rcases n wit... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_14 | 7dc898163475c649 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 4 | [
{
"theorem_name": "append_left_injective",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply List.ext_getElem hl\n intros\n rw [← get_append_left, ← get_append_left, h]",
"n_chars": 91,
"n_subpr... | [
{
"name": "get_append_left",
"text": "lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by\n induction x generalizing n with\n | nil => simp at h\n | cons b x ih =>\n rcases n with (_ | n)\n · simp\n · simp [ih n (by simpa using h), cons_append_ωSequence]\n\n",
"fan_in": 4,
... | [
{
"name": "drop_append_of_le_length",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 10,
"n_chars": 475,
"n_subproofs": 3,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -195,6 +195,14 @@
| List.cons a l₁, l₂, s => by
rw [List.cons_append, cons_append_ωSequence, cons_append_ωSequence, append_append_ωSequence l₁]
+lemma get_append_left (h : n < x.length) : (x ++ω a) n = x[n] := by
+ induction x generalizing n with
+ | nil => simp at h
+ | cons b x ih =>
+ rcases n wit... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_15 | 0743a209a8121ff8 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "drop_append_of_ge_length",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext k; simp (disch := omega) only [get_drop, get_append_right']\n congr; omega",
"n_chars": 84,
"n_subpro... | [
{
"name": "get_append_right'",
"text": "theorem get_append_right' {xl : List α} {xs : ωSequence α} {k : ℕ} (h : xl.length ≤ k) :\n (xl ++ω xs) k = xs (k - xl.length) := by\n obtain ⟨n, rfl⟩ := show ∃ n, k = xl.length + n by use (k - xl.length); omega\n simp only [Nat.add_sub_cancel_left]; apply get_app... | [
{
"name": "drop_append_of_ge_length",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 8,
"n_chars": 367,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -207,6 +207,11 @@
lemma get_append_right : (x ++ω a) (x.length + n) = a n := by
induction x <;> simp [Nat.succ_add, *, cons_append_ωSequence]
+theorem get_append_right' {xl : List α} {xs : ωSequence α} {k : ℕ} (h : xl.length ≤ k) :
+ (xl ++ω xs) k = xs (k - xl.length) := by
+ obtain ⟨n, rfl⟩ := show ∃ n, k... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_16 | 89e8c58bd0859498 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "take_theorem",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext n\n induction n with\n | zero => simpa [take] using h 1\n | succ n =>\n have h₁ : some (s₁ (succ n)) = some (s₂ (suc... | [
{
"name": "getElem?_take_succ",
"text": "theorem getElem?_take_succ (n : ℕ) (s : ωSequence α) :\n (take (succ n) s)[n]? = some (s n) :=\n getElem?_take (Nat.lt_succ_self n)\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 139,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_... | [
{
"name": "take_theorem",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 353,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -276,6 +276,10 @@
| k+1, n+1, h => by
rw [take_succ, List.getElem?_cons_succ, getElem?_take (Nat.lt_of_succ_lt_succ h), get_succ k s]
+theorem getElem?_take_succ (n : ℕ) (s : ωSequence α) :
+ (take (succ n) s)[n]? = some (s n) :=
+ getElem?_take (Nat.lt_succ_self n)
+
@[simp, scoped grind =]
theorem ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_17 | 5499a18c6e092b87 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 10 | [
{
"theorem_name": "extract_eq_ofFn",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext k; cases Decidable.em (k < n - m) <;>\n grind [extract_eq_drop_take, getElem?_take]",
"n_chars": 93,
"n_subpro... | [
{
"name": "extract_eq_drop_take",
"text": "theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :\n xs.extract m n = take (n - m) (xs.drop m) := by\n rfl\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 123,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": ... | [
{
"name": "extract_eq_ofFn",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 224,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -305,11 +305,18 @@
lemma take_prefix : a.take m <+: a.take n ↔ m ≤ n :=
⟨fun h ↦ by simpa using h.length_le, take_prefix_take_left m n a⟩
+theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :
+ xs.extract m n = take (n - m) (xs.drop m) := by
+ rfl
+
theorem extract_eq_ofFn {xs : ωSequence α} {m n :... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_18 | 9f2e9caca2ada0dd | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 10 | [
{
"theorem_name": "extract_eq_ofFn",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext k; cases Decidable.em (k < n - m) <;>\n grind [extract_eq_drop_take, getElem?_take]",
"n_chars": 93,
"n_subpro... | [
{
"name": "extract_eq_drop_take",
"text": "theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :\n xs.extract m n = take (n - m) (xs.drop m) := by\n rfl\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 123,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": ... | [
{
"name": "extract_eq_extract",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 353,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -305,8 +305,14 @@
lemma take_prefix : a.take m <+: a.take n ↔ m ≤ n :=
⟨fun h ↦ by simpa using h.length_le, take_prefix_take_left m n a⟩
+theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :
+ xs.extract m n = take (n - m) (xs.drop m) := by
+ rfl
+
theorem extract_eq_ofFn {xs : ωSequence α} {m n : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_19 | ad3ddc45bf4d2c76 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 10 | [
{
"theorem_name": "extract_eq_ofFn",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext k; cases Decidable.em (k < n - m) <;>\n grind [extract_eq_drop_take, getElem?_take]",
"n_chars": 93,
"n_subpro... | [
{
"name": "extract_eq_drop_take",
"text": "theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :\n xs.extract m n = take (n - m) (xs.drop m) := by\n rfl\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 123,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": ... | [
{
"name": "extract_append_right_right",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 5,
"n_chars": 245,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"m... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -317,11 +317,18 @@
-- Take theorem reduces a proof of equality of infinite ω-sequences to an
-- induction over all their finite approximations.
+theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :
+ xs.extract m n = take (n - m) (xs.drop m) := by
+ rfl
+
theorem extract_eq_ofFn {xs : ωSequence α} {m... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_20 | 53bb9412043d65b9 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 10 | [
{
"theorem_name": "extract_eq_ofFn",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext k; cases Decidable.em (k < n - m) <;>\n grind [extract_eq_drop_take, getElem?_take]",
"n_chars": 93,
"n_subpro... | [
{
"name": "extract_eq_drop_take",
"text": "theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :\n xs.extract m n = take (n - m) (xs.drop m) := by\n rfl\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 123,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": ... | [
{
"name": "extract_append_zero_right",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 303,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"m... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -308,11 +308,18 @@
lemma take_prefix : a.take m <+: a.take n ↔ m ≤ n :=
⟨fun h ↦ by simpa using h.length_le, take_prefix_take_left m n a⟩
+theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :
+ xs.extract m n = take (n - m) (xs.drop m) := by
+ rfl
+
theorem extract_eq_ofFn {xs : ωSequence α} {m n :... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_21 | a880c13528066003 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 10 | [
{
"theorem_name": "extract_eq_ofFn",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext k; cases Decidable.em (k < n - m) <;>\n grind [extract_eq_drop_take, getElem?_take]",
"n_chars": 93,
"n_subpro... | [
{
"name": "extract_eq_drop_take",
"text": "theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :\n xs.extract m n = take (n - m) (xs.drop m) := by\n rfl\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 123,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": ... | [
{
"name": "extract_drop",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -305,11 +305,18 @@
lemma take_prefix : a.take m <+: a.take n ↔ m ≤ n :=
⟨fun h ↦ by simpa using h.length_le, take_prefix_take_left m n a⟩
+theorem extract_eq_drop_take {xs : ωSequence α} {m n : ℕ} :
+ xs.extract m n = take (n - m) (xs.drop m) := by
+ rfl
+
theorem extract_eq_ofFn {xs : ωSequence α} {m n :... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f2d925b57d1b_22 | b7f04a64e90a0997 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Init.lean | Init | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "append_left_right_injective",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h3 := append_left_injective l1 l2 s1 s2 h1 h2\n grind",
"n_chars": 64,
"n_subproofs": 1,
"n_t... | [
{
"name": "append_left_injective",
"text": "lemma append_left_injective (h : x ++ω a = y ++ω b) (hl : x.length = y.length) : x = y := by\n apply List.ext_getElem hl\n intros\n rw [← get_append_left, ← get_append_left, h]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 184,
"n_subproofs": 0,
... | [
{
"name": "append_extract_extract",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 6,
"n_chars": 255,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_... | 4 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Fabrizio Montesi
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order... | @@ -217,6 +217,11 @@
lemma append_right_inj : x ++ω a = x ++ω b ↔ a = b :=
⟨append_right_injective x a b, by simp +contextual⟩
+lemma append_left_injective (h : x ++ω a = y ++ω b) (hl : x.length = y.length) : x = y := by
+ apply List.ext_getElem hl
+ intros
+ rw [← get_append_left, ← get_append_left, h]
+
the... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f1be41b27e26_0 | 25ec654f2de87736 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "MTr.stepR",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h1 h2\n induction h1\n case refl s1' => exact MTr.single lts h2\n case stepL s1' μ' s2' μs' s3' h1' h3 ih =>\n apply ... | [
{
"name": "MTr.single",
"text": "/-- Any transition is also a multistep transition. -/\n@[scoped grind →]\ntheorem MTr.single {s1 : State} {μ : Label} {s2 : State} :\n lts.Tr s1 μ s2 → lts.MTr s1 [μ] s2 := by\n intro h\n apply MTr.stepL\n · exact h\n · apply MTr.refl\n\n",
"fan_in": 2,
"n_lines... | [
{
"name": "MTr.stepR",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 417,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"max_nesting": 4
... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | @@ -95,9 +95,25 @@
@[simp] theorem MTr.nil_iff (s1 s2 : State) : lts.MTr s1 [] s2 ↔ s1 = s2 :=
⟨nil_eq lts, fun h => h ▸ MTr.refl⟩
+/-- Any transition is also a multistep transition. -/
+@[scoped grind →]
+theorem MTr.single {s1 : State} {μ : Label} {s2 : State} :
+ lts.Tr s1 μ s2 → lts.MTr s1 [μ] s2 := by
+ in... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f1be41b27e26_1 | e889f57d8952de34 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "MTr.singleton_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " ⟨MTr.single_invert lts s1 μ s2, MTr.single lts⟩",
"n_chars": 53,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic"... | [
{
"name": "MTr.single_invert",
"text": "/-- Any 1-sized multistep transition implies a transition with the same states and label. -/\n@[scoped grind .]\ntheorem MTr.single_invert (s1 : State) (μ : Label) (s2 : State) :\n lts.MTr s1 [μ] s2 → lts.Tr s1 μ s2 := by\n intro h\n cases h\n case stepL s1' htr h... | [
{
"name": "MTr.singleton_iff",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 264,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | @@ -117,9 +117,19 @@
· exact h1'
· apply ih h2
+/-- Any 1-sized multistep transition implies a transition with the same states and label. -/
+@[scoped grind .]
+theorem MTr.single_invert (s1 : State) (μ : Label) (s2 : State) :
+ lts.MTr s1 [μ] s2 → lts.Tr s1 μ s2 := by
+ intro h
+ cases h
+ case stepL s... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f1be41b27e26_2 | 92adbeed9bb76a00 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "MTr.append_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨MTr.split, ?_⟩\n intro ⟨_, h, h'⟩\n exact h.comp lts h'",
"n_chars": 77,
"n_subproofs": 0,
"n_tactics"... | [
{
"name": "MTr.split",
"text": "/-- A multistep transition over a concatenation can be split into two multistep transitions. -/\ntheorem MTr.split {lts : LTS State Label} (h : lts.MTr s1 (μs ++ μs') s2) :\n ∃ s, lts.MTr s1 μs s ∧ lts.MTr s μs' s2 := by\n induction μs generalizing s1 s2 with\n | nil => ... | [
{
"name": "MTr.append_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 336,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | @@ -131,9 +131,24 @@
@[simp] theorem MTr.singleton_iff (s1 : State) (μ : Label) (s2 : State) :
lts.MTr s1 [μ] s2 ↔ lts.Tr s1 μ s2 := ⟨MTr.single_invert lts s1 μ s2, MTr.single lts⟩
+/-- A multistep transition over a concatenation can be split into two multistep transitions. -/
+theorem MTr.split {lts : LTS State ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f1be41b27e26_3 | e7a166a79118a3df | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "mem_foldl_setImage",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← setImageMultistep_foldl_setImage]\n exact mem_setImageMultistep",
"n_chars": 77,
"n_subproofs": 0,
"n... | [
{
"name": "setImageMultistep_foldl_setImage",
"text": "/-- Characterisation of `setImageMultistep` as `List.foldl` on `setImage`. -/\n@[scoped grind _=_]\ntheorem setImageMultistep_foldl_setImage (lts : LTS State Label) :\n lts.setImageMultistep = List.foldl lts.setImage := by\n ext S μs s'\n induction μ... | [
{
"name": "mem_foldl_setImage",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 304,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Init
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.SetNotation
/-!
# Labelled Transition System (LTS)
A L... | @@ -221,10 +221,19 @@
lemma setImageMultistep_setImage_head (lts : LTS State Label) :
lts.setImageMultistep S (μ :: μs) = lts.setImageMultistep (lts.setImage S μ ) μs := by grind
+/-- Characterisation of `setImageMultistep` as `List.foldl` on `setImage`. -/
+@[scoped grind _=_]
+theorem setImageMultistep_foldl_se... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_598021f936a4_0 | a5c6cc8de45e32e5 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/OmegaExecution.lean | OmegaExecution | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "OmegaExecution.extract_mTr",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n grind [OmegaExecution.extract_execution h hnm]",
"n_chars": 52,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "OmegaExecution.extract_execution",
"text": "/-- Any finite execution extracted from an infinite execution is valid. -/\ntheorem OmegaExecution.extract_execution\n (h : lts.OmegaExecution ss μs) {n m : ℕ} (hnm : n ≤ m) :\n lts.Execution (ss n) (μs.extract n m) (ss m) (ss.extract n (m + 1)) :... | [
{
"name": "OmegaExecution.extract_mTr",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 280,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"m... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Cslib.Foundations.Semantics.LTS.Execution
/-!
# Infinite execu... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Cslib.Foundations.Semantics.LTS.Execution
/-!
# Infinite execu... | @@ -28,10 +28,17 @@
variable {State Label : Type*} {lts : LTS State Label}
+/-- Any finite execution extracted from an infinite execution is valid. -/
+theorem OmegaExecution.extract_execution
+ (h : lts.OmegaExecution ss μs) {n m : ℕ} (hnm : n ≤ m) :
+ lts.Execution (ss n) (μs.extract n m) (ss m) (ss.extrac... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_a5b081a52cee_0 | f836acdc9b9e900f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Logics/Modal/Denotation.lean | Denotation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "not_denotation",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n grind [_=_ satisfies_mem_denotation]",
"n_chars": 42,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
... | [
{
"name": "satisfies_mem_denotation",
"text": "/-- Characterisation theorem for the denotational semantics. -/\n@[scoped grind =]\ntheorem satisfies_mem_denotation {m : Model World Atom} {φ : Proposition Atom} :\n w ∈ φ.denotation m ↔ ⇓Modal[m,w ⊨ φ] := by\n induction φ generalizing w <;> grind\n\n",
... | [
{
"name": "not_denotation",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 313,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Logics.Modal.Basic
/-! # Denotational semantics for Modal Logic
A denotational semantics for modal logic, inspired by the one for H... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Logics.Modal.Basic
/-! # Denotational semantics for Modal Logic
A denotational semantics for modal logic, inspired by the one for H... | @@ -29,11 +29,18 @@
| .and φ₁ φ₂ => φ₁.denotation m ∩ φ₂.denotation m
| .diamond φ => {w | ∃ w', m.r w w' ∧ w' ∈ φ.denotation m}
+/-- Characterisation theorem for the denotational semantics. -/
+@[scoped grind =]
+theorem satisfies_mem_denotation {m : Model World Atom} {φ : Proposition Atom} :
+ w ∈ φ.denota... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_a5b081a52cee_1 | 01a63ff68502b454 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Logics/Modal/Denotation.lean | Denotation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "not_denotation",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n grind [_=_ satisfies_mem_denotation]",
"n_chars": 42,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
... | [
{
"name": "satisfies_mem_denotation",
"text": "/-- Characterisation theorem for the denotational semantics. -/\n@[scoped grind =]\ntheorem satisfies_mem_denotation {m : Model World Atom} {φ : Proposition Atom} :\n w ∈ φ.denotation m ↔ ⇓Modal[m,w ⊨ φ] := by\n induction φ generalizing w <;> grind\n\n",
... | [
{
"name": "theoryEq_denotation_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 346,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Logics.Modal.Basic
/-! # Denotational semantics for Modal Logic
A denotational semantics for modal logic, inspired by the one for H... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi
-/
module
public import Cslib.Logics.Modal.Basic
/-! # Denotational semantics for Modal Logic
A denotational semantics for modal logic, inspired by the one for H... | @@ -29,16 +29,24 @@
| .and φ₁ φ₂ => φ₁.denotation m ∩ φ₂.denotation m
| .diamond φ => {w | ∃ w', m.r w w' ∧ w' ∈ φ.denotation m}
+/-- Characterisation theorem for the denotational semantics. -/
+@[scoped grind =]
+theorem satisfies_mem_denotation {m : Model World Atom} {φ : Proposition Atom} :
+ w ∈ φ.denota... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c09b1cc7836b_0 | b9874fad854b7dae | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/PFunctor/Free.lean | Free | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "Interprets.eq",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext x\n induction x with\n | pure a => exact h.apply_pure a\n | lift_bind a cont ih =>\n rw [h.apply_lift_bind]\n co... | [
{
"name": "bind_eq_bind",
"text": "/-- Note that this lemma does not always apply, as it is universe-constrained by `Bind.bind`. -/\n@[simp]\ntheorem bind_eq_bind {α β : Type v} :\n (FreeM.bind : P.FreeM α → _ → P.FreeM β) = Bind.bind := rfl\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 216,
... | [
{
"name": "Interprets.eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 353,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Cslib.Init
public import Mathlib.Data.PFunctor.Univariate.Basic
/-!
# Free Monad of a Polynomial Functor
We define the free monad on a **polynomial fun... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Cslib.Init
public import Mathlib.Data.PFunctor.Univariate.Basic
/-!
# Free Monad of a Polynomial Functor
We define the free monad on a **polynomial fun... | @@ -108,6 +108,11 @@
instance : Bind (P.FreeM) where bind := .bind
+/-- Note that this lemma does not always apply, as it is universe-constrained by `Bind.bind`. -/
+@[simp]
+theorem bind_eq_bind {α β : Type v} :
+ (FreeM.bind : P.FreeM α → _ → P.FreeM β) = Bind.bind := rfl
+
/-- Map a function over a `FreeM` ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c09b1cc7836b_1 | 61738ca4815e842a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/PFunctor/Free.lean | Free | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "Interprets.eq",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext x\n induction x with\n | pure a => exact h.apply_pure a\n | lift_bind a cont ih =>\n rw [h.apply_lift_bind]\n co... | [
{
"name": "bind_eq_bind",
"text": "/-- Note that this lemma does not always apply, as it is universe-constrained by `Bind.bind`. -/\n@[simp]\ntheorem bind_eq_bind {α β : Type v} :\n (FreeM.bind : P.FreeM α → _ → P.FreeM β) = Bind.bind := rfl\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 216,
... | [
{
"name": "liftM_bind",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 6,
"n_lines": 14,
"n_chars": 446,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Cslib.Init
public import Mathlib.Data.PFunctor.Univariate.Basic
/-!
# Free Monad of a Polynomial Functor
We define the free monad on a **polynomial fun... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Cslib.Init
public import Mathlib.Data.PFunctor.Univariate.Basic
/-!
# Free Monad of a Polynomial Functor
We define the free monad on a **polynomial fun... | @@ -108,6 +108,11 @@
instance : Bind (P.FreeM) where bind := .bind
+/-- Note that this lemma does not always apply, as it is universe-constrained by `Bind.bind`. -/
+@[simp]
+theorem bind_eq_bind {α β : Type v} :
+ (FreeM.bind : P.FreeM α → _ → P.FreeM β) = Bind.bind := rfl
+
/-- Map a function over a `FreeM` ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_0 | 1799e27914d9688e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 6 | [
{
"theorem_name": "isChurchListPair_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · apply isChurchList_trans (MRed.tail Fst hp)\n exact hp'.1\n · apply isChurchList_trans (MRed.ta... | [
{
"name": "isChurchList_trans",
"text": "/-- `IsChurchList` is preserved under multi-step reduction of the term. -/\ntheorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')\n (hcns' : IsChurchList ns cns') : IsChurchList ns cns := by\n match ns with\n | [] =>\n intro c n\n exac... | [
{
"name": "isChurchListPair_trans",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 381,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -32,6 +32,18 @@
∃ cx cxs : SKI, IsChurch x cx ∧ IsChurchList xs cxs ∧
(cns ⬝ c ⬝ n) ↠ c ⬝ cx ⬝ (cxs ⬝ c ⬝ n)
+/-- `IsChurchList` is preserved under multi-step reduction of the term. -/
+theorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')
+ (hcns' : IsChurchList ns cns') : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_1 | aaed027ca77f8deb | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "nil_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " nil_def",
"n_chars": 8,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0... | [
{
"name": "nil_def",
"text": "/-- Reduction: `Nil ⬝ c ⬝ n ↠ n`. -/\ntheorem nil_def (c n : SKI) : (Nil ⬝ c ⬝ n) ↠ n :=\n NilPoly.toSKI_correct [c, n] (by simp)\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 142,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
... | [
{
"name": "nil_correct",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 157,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -69,8 +69,12 @@
/-- The SKI term for the empty list. -/
def Nil : SKI := NilPoly.toSKI
+/-- Reduction: `Nil ⬝ c ⬝ n ↠ n`. -/
+theorem nil_def (c n : SKI) : (Nil ⬝ c ⬝ n) ↠ n :=
+ NilPoly.toSKI_correct [c, n] (by simp)
+
/-- The empty list term correctly represents `[]`. -/
-theorem nil_correct : IsChurchList [... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_2 | 4ae02c7706c2252f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "cons_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro c n\n use cx, cxs, hcx, hcxs\n exact cons_def cx cxs c n",
"n_chars": 68,
"n_subproofs": 0,
"n_tactics": 4... | [
{
"name": "cons_def",
"text": "/-- Reduction: `Cons ⬝ x ⬝ xs ⬝ c ⬝ n ↠ c ⬝ x ⬝ (xs ⬝ c ⬝ n)`. -/\ntheorem cons_def (x xs c n : SKI) :\n (Cons ⬝ x ⬝ xs ⬝ c ⬝ n) ↠ c ⬝ x ⬝ (xs ⬝ c ⬝ n) :=\n ConsPoly.toSKI_correct [x, xs, c, n] (by simp)\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 242,
"n_s... | [
{
"name": "cons_correct",
"fan_in": 5,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 290,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -84,10 +84,18 @@
/-- The SKI term for list cons. -/
def Cons : SKI := ConsPoly.toSKI
+/-- Reduction: `Cons ⬝ x ⬝ xs ⬝ c ⬝ n ↠ c ⬝ x ⬝ (xs ⬝ c ⬝ n)`. -/
+theorem cons_def (x xs c n : SKI) :
+ (Cons ⬝ x ⬝ xs ⬝ c ⬝ n) ↠ c ⬝ x ⬝ (xs ⬝ c ⬝ n) :=
+ ConsPoly.toSKI_correct [x, xs, c, n] (by simp)
+
/-- Cons preserv... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_3 | 1093cc6c424ed9df | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 4 | [
{
"theorem_name": "singleton_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n cons_correct hcx nil_correct",
"n_chars": 31,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_auto... | [
{
"name": "nil_correct",
"text": "/-- The empty list term correctly represents `[]`. -/\ntheorem nil_correct : IsChurchList [] Nil := nil_def\n\n/-! ### Cons: Consing an element onto a list -/\n\n",
"fan_in": 4,
"n_lines": 6,
"n_chars": 157,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "singleton_correct",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 184,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 4 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -73,6 +73,11 @@
theorem nil_def (c n : SKI) : (Nil ⬝ c ⬝ n) ↠ n :=
NilPoly.toSKI_correct [c, n] (by simp)
+/-- The empty list term correctly represents `[]`. -/
+theorem nil_correct : IsChurchList [] Nil := nil_def
+
+/-! ### Cons: Consing an element onto a list -/
+
/-- cons = λ x xs c n. c x (xs c n) -/
de... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_4 | 1972bd5c10a0093e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 4 | [
{
"theorem_name": "singleton_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n cons_correct hcx nil_correct",
"n_chars": 31,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_auto... | [
{
"name": "nil_correct",
"text": "/-- The empty list term correctly represents `[]`. -/\ntheorem nil_correct : IsChurchList [] Nil := nil_def\n\n/-! ### Cons: Consing an element onto a list -/\n\n",
"fan_in": 4,
"n_lines": 6,
"n_chars": 157,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "toChurch_correct",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 9,
"n_chars": 289,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nestin... | 4 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -73,6 +73,11 @@
theorem nil_def (c n : SKI) : (Nil ⬝ c ⬝ n) ↠ n :=
NilPoly.toSKI_correct [c, n] (by simp)
+/-- The empty list term correctly represents `[]`. -/
+theorem nil_correct : IsChurchList [] Nil := nil_def
+
+/-! ### Cons: Consing an element onto a list -/
+
/-- cons = λ x xs c n. c x (xs c n) -/
de... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_5 | 3ece60d5e3daf9d4 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "headD_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n match ns with\n | [] =>\n simp only [List.headD_nil]\n apply isChurch_trans d (headD_def cd cns)\n apply isChurch_... | [
{
"name": "headD_def",
"text": "/-- Reduction: `HeadD ⬝ d ⬝ xs ↠ xs ⬝ K ⬝ d`. -/\ntheorem headD_def (d xs : SKI) : (HeadD ⬝ d ⬝ xs) ↠ xs ⬝ K ⬝ d :=\n HeadDPoly.toSKI_correct [d, xs] (by simp)\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 180,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "headD_correct",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 600,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -104,13 +104,25 @@
/-- The SKI term for list head with default. -/
def HeadD : SKI := HeadDPoly.toSKI
+/-- Reduction: `HeadD ⬝ d ⬝ xs ↠ xs ⬝ K ⬝ d`. -/
+theorem headD_def (d xs : SKI) : (HeadD ⬝ d ⬝ xs) ↠ xs ⬝ K ⬝ d :=
+ HeadDPoly.toSKI_correct [d, xs] (by simp)
+
/-- General head-with-default correctness. -/
... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_6 | a4ce553d6553ca3a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "headD_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n match ns with\n | [] =>\n simp only [List.headD_nil]\n apply isChurch_trans d (headD_def cd cns)\n apply isChurch_... | [
{
"name": "headD_def",
"text": "/-- Reduction: `HeadD ⬝ d ⬝ xs ↠ xs ⬝ K ⬝ d`. -/\ntheorem headD_def (d xs : SKI) : (HeadD ⬝ d ⬝ xs) ↠ xs ⬝ K ⬝ d :=\n HeadDPoly.toSKI_correct [d, xs] (by simp)\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 180,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "head_def",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -104,11 +104,16 @@
/-- The SKI term for list head with default. -/
def HeadD : SKI := HeadDPoly.toSKI
+/-- Reduction: `HeadD ⬝ d ⬝ xs ↠ xs ⬝ K ⬝ d`. -/
+theorem headD_def (d xs : SKI) : (HeadD ⬝ d ⬝ xs) ↠ xs ⬝ K ⬝ d :=
+ HeadDPoly.toSKI_correct [d, xs] (by simp)
+
/-- The SKI term for list head (default 0). -/... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_7 | 9022b69621f321d8 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "headD_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n match ns with\n | [] =>\n simp only [List.headD_nil]\n apply isChurch_trans d (headD_def cd cns)\n apply isChurch_... | [
{
"name": "headD_def",
"text": "/-- Reduction: `HeadD ⬝ d ⬝ xs ↠ xs ⬝ K ⬝ d`. -/\ntheorem headD_def (d xs : SKI) : (HeadD ⬝ d ⬝ xs) ↠ xs ⬝ K ⬝ d :=\n HeadDPoly.toSKI_correct [d, xs] (by simp)\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 180,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "head_correct",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 241,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": ... | 2 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -104,13 +104,25 @@
/-- The SKI term for list head with default. -/
def HeadD : SKI := HeadDPoly.toSKI
+/-- Reduction: `HeadD ⬝ d ⬝ xs ↠ xs ⬝ K ⬝ d`. -/
+theorem headD_def (d xs : SKI) : (HeadD ⬝ d ⬝ xs) ↠ xs ⬝ K ⬝ d :=
+ HeadDPoly.toSKI_correct [d, xs] (by simp)
+
/-- General head-with-default correctness. -/
... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_8 | c2bfcc6d4a8ce177 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 6 | [
{
"theorem_name": "isChurchListPair_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · apply isChurchList_trans (MRed.tail Fst hp)\n exact hp'.1\n · apply isChurchList_trans (MRed.ta... | [
{
"name": "isChurchList_trans",
"text": "/-- `IsChurchList` is preserved under multi-step reduction of the term. -/\ntheorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')\n (hcns' : IsChurchList ns cns') : IsChurchList ns cns := by\n match ns with\n | [] =>\n intro c n\n exac... | [
{
"name": "tailStep_correct",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 9,
"n_chars": 437,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 5 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -32,6 +32,18 @@
∃ cx cxs : SKI, IsChurch x cx ∧ IsChurchList xs cxs ∧
(cns ⬝ c ⬝ n) ↠ c ⬝ cx ⬝ (cxs ⬝ c ⬝ n)
+/-- `IsChurchList` is preserved under multi-step reduction of the term. -/
+theorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')
+ (hcns' : IsChurchList ns cns') : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_9 | f4fe07daee632445 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 6 | [
{
"theorem_name": "isChurchListPair_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · apply isChurchList_trans (MRed.tail Fst hp)\n exact hp'.1\n · apply isChurchList_trans (MRed.ta... | [
{
"name": "isChurchList_trans",
"text": "/-- `IsChurchList` is preserved under multi-step reduction of the term. -/\ntheorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')\n (hcns' : IsChurchList ns cns') : IsChurchList ns cns := by\n match ns with\n | [] =>\n intro c n\n exac... | [
{
"name": "tailFold_correct",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 27,
"n_chars": 1250,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 4,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 11,
"automation_only": false,
"max_ne... | 9 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -32,6 +32,18 @@
∃ cx cxs : SKI, IsChurch x cx ∧ IsChurchList xs cxs ∧
(cns ⬝ c ⬝ n) ↠ c ⬝ cx ⬝ (cxs ⬝ c ⬝ n)
+/-- `IsChurchList` is preserved under multi-step reduction of the term. -/
+theorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')
+ (hcns' : IsChurchList ns cns') : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_10 | 4f23258b54e1a904 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "tailStep_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply isChurchListPair_trans (tailStep_def cx p)\n exact ⟨isChurchList_trans (fst_correct _ _) hp.2,\n isChurchLi... | [
{
"name": "isChurchListPair_trans",
"text": "/-- IsChurchListPair is preserved under reduction. -/\n@[scoped grind →]\ntheorem isChurchListPair_trans {prev curr : List ℕ} {p p' : SKI} (hp : p ↠ p')\n (hp' : IsChurchListPair prev curr p') : IsChurchListPair prev curr p := by\n constructor\n · apply isCh... | [
{
"name": "tail_correct",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 11,
"n_lines": 15,
"n_chars": 590,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nesting"... | 11 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -49,6 +49,16 @@
fst : IsChurchList prev (Fst ⬝ p)
snd : IsChurchList curr (Snd ⬝ p)
+/-- IsChurchListPair is preserved under reduction. -/
+@[scoped grind →]
+theorem isChurchListPair_trans {prev curr : List ℕ} {p p' : SKI} (hp : p ↠ p')
+ (hp' : IsChurchListPair prev curr p') : IsChurchListPair prev curr... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_11 | d267f6f7eda23f92 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 6 | [
{
"theorem_name": "isChurchListPair_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · apply isChurchList_trans (MRed.tail Fst hp)\n exact hp'.1\n · apply isChurchList_trans (MRed.ta... | [
{
"name": "isChurchList_trans",
"text": "/-- `IsChurchList` is preserved under multi-step reduction of the term. -/\ntheorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')\n (hcns' : IsChurchList ns cns') : IsChurchList ns cns := by\n match ns with\n | [] =>\n intro c n\n exac... | [
{
"name": "prependZero_correct",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 9,
"n_chars": 343,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nes... | 4 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -32,6 +32,18 @@
∃ cx cxs : SKI, IsChurch x cx ∧ IsChurchList xs cxs ∧
(cns ⬝ c ⬝ n) ↠ c ⬝ cx ⬝ (cxs ⬝ c ⬝ n)
+/-- `IsChurchList` is preserved under multi-step reduction of the term. -/
+theorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')
+ (hcns' : IsChurchList ns cns') : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2f5ad412705e_12 | d5b006aeb12d8356 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/List.lean | List | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 6 | [
{
"theorem_name": "isChurchListPair_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · apply isChurchList_trans (MRed.tail Fst hp)\n exact hp'.1\n · apply isChurchList_trans (MRed.ta... | [
{
"name": "isChurchList_trans",
"text": "/-- `IsChurchList` is preserved under multi-step reduction of the term. -/\ntheorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')\n (hcns' : IsChurchList ns cns') : IsChurchList ns cns := by\n match ns with\n | [] =>\n intro c n\n exac... | [
{
"name": "succHead_correct",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 8,
"n_lines": 9,
"n_chars": 464,
"n_subproofs": 2,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 8 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Church-Encoded Lists in SKI Combinatory Logic
Church-encoded lists for proving SKI ≃ TM equivalenc... | @@ -32,6 +32,18 @@
∃ cx cxs : SKI, IsChurch x cx ∧ IsChurchList xs cxs ∧
(cns ⬝ c ⬝ n) ↠ c ⬝ cx ⬝ (cxs ⬝ c ⬝ n)
+/-- `IsChurchList` is preserved under multi-step reduction of the term. -/
+theorem isChurchList_trans {ns : List ℕ} {cns cns' : SKI} (h : cns ↠ cns')
+ (hcns' : IsChurchList ns cns') : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_5b4f4e129a83_3 | e6b047192f8d9899 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Subtype.lean | Subtype | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "trans",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro sub₁ sub₂\n have δ_lc : δ.LC := by grind\n induction δ_lc generalizing Γ σ τ\n case top => cases sub₁ <;> cases sub₂ <;> gr... | [
{
"name": "narrow_aux",
"text": "lemma narrow_aux\n (trans : ∀ Γ σ τ, Sub Γ σ δ → Sub Γ δ τ → Sub Γ σ τ)\n (sub₁ : Sub (Γ ++ ⟨X, Binding.sub δ⟩ :: Δ) σ τ) (sub₂ : Sub Δ δ' δ) :\n Sub (Γ ++ ⟨X, Binding.sub δ'⟩ :: Δ) σ τ := by\n generalize eq : Γ ++ ⟨X, Binding.sub δ⟩ :: Δ = Θ at sub₁\n induction... | [
{
"name": "map_subst",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 7,
"n_lines": 18,
"n_chars": 932,
"n_subproofs": 4,
"n_tactics": 16,
"cyclomatic": 4,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 4... | 5 | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.WellFormed
/-! # λ-calculus
The λ-calculus with polymorphism and subtyping, with a locally na... | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.WellFormed
/-! # λ-calculus
The λ-calculus with polymorphism and subtyping, with a locally na... | @@ -77,6 +77,30 @@
have eq : Γ ++ Δ = [] ++ Γ ++ Δ := by grind
grind [weaken]
+lemma narrow_aux
+ (trans : ∀ Γ σ τ, Sub Γ σ δ → Sub Γ δ τ → Sub Γ σ τ)
+ (sub₁ : Sub (Γ ++ ⟨X, Binding.sub δ⟩ :: Δ) σ τ) (sub₂ : Sub Δ δ' δ) :
+ Sub (Γ ++ ⟨X, Binding.sub δ'⟩ :: Δ) σ τ := by
+ generalize eq : Γ ++ ⟨X, Bi... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_18d03320f2e3_0 | 949239d6d15309ae | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Stlc/StrongNorm.lean | StrongNorm | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "strong_norm",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (semanticMap_saturated τ).sn\n apply (soundness der [] (by grind) entailsContext_empty)",
"n_chars": 100,
"n_sub... | [
{
"name": "soundness",
"text": "/-- The `soundness` lemma states that if a term `t` has type `τ` in context `Γ`,\n then `t` is semantically valid with respect to `Γ` and `τ` -/\nlemma soundness {Γ : Context Var (Ty Base)} (derivation_t : Γ ⊢ t ∶ τ) : entails Γ t τ := by\n induction derivation_t with\n ... | [
{
"name": "strong_norm",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 357,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2... | 2 | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Foundations.Data.HasFresh
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Stlc.Basic
public import Cslib.Languages.LambdaCalcu... | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Foundations.Data.HasFresh
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Stlc.Basic
public import Cslib.Languages.LambdaCalcu... | @@ -100,10 +100,28 @@
abbrev entails (Γ : Context Var (Ty Base)) (t : Term Var) (τ : Ty Base) :=
∀ E, envLC E → entailsContext E Γ → multiSubst E t ∈ semanticMap τ
+/-- The `soundness` lemma states that if a term `t` has type `τ` in context `Γ`,
+ then `t` is semantically valid with respect to `Γ` and `τ` -/... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_180fbfcdbacc_5 | 47a233f88520543a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/StandardForm.lean | StandardForm | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "Halts.toStandardForm",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨s, hsteps, hhalted⟩ := h\n obtain ⟨s₂, hsteps₂, hhalted₂, _⟩ := Steps.toStandardForm_halts hsteps hhalted\n ... | [
{
"name": "Steps.toStandardForm_halts",
"text": "/-- Forward halting: if p reaches a halted state, p.toStandardForm reaches a halted state\n with the same registers. -/\ntheorem Steps.toStandardForm_halts {p : Program} {s s' : State}\n (hsteps : Steps p s s') (hhalted : s'.isHalted p) :\n ∃ s₂, Ste... | [
{
"name": "eval_toStandardForm",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 12,
"n_chars": 423,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_ne... | 6 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.StraightLine
/-! # Standard Form Programs
This file defines standard-form programs (those with bounded jump targets)
and pro... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.StraightLine
/-! # Standard Form Programs
This file defines standard-form programs (those with bounded jump targets)
and pro... | @@ -100,9 +100,30 @@
· use ⟨p.length, s.regs⟩
grind [State.isHalted, Program.toStandardForm_length]
+/-- Forward halting: if p reaches a halted state, p.toStandardForm reaches a halted state
+ with the same registers. -/
+theorem Steps.toStandardForm_halts {p : Program} {s s' : State}
+ (hsteps ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_180fbfcdbacc_6 | dbe4b58942e414e1 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/StandardForm.lean | StandardForm | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "Halts.toStandardForm",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨s, hsteps, hhalted⟩ := h\n obtain ⟨s₂, hsteps₂, hhalted₂, _⟩ := Steps.toStandardForm_halts hsteps hhalted\n ... | [
{
"name": "Steps.toStandardForm_halts",
"text": "/-- Forward halting: if p reaches a halted state, p.toStandardForm reaches a halted state\n with the same registers. -/\ntheorem Steps.toStandardForm_halts {p : Program} {s s' : State}\n (hsteps : Steps p s s') (hhalted : s'.isHalted p) :\n ∃ s₂, Ste... | [
{
"name": "toStandardForm_equiv",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 10,
"n_lines": 5,
"n_chars": 161,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_n... | 7 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.StraightLine
/-! # Standard Form Programs
This file defines standard-form programs (those with bounded jump targets)
and pro... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.StraightLine
/-! # Standard Form Programs
This file defines standard-form programs (those with bounded jump targets)
and pro... | @@ -100,9 +100,30 @@
· use ⟨p.length, s.regs⟩
grind [State.isHalted, Program.toStandardForm_length]
+/-- Forward halting: if p reaches a halted state, p.toStandardForm reaches a halted state
+ with the same registers. -/
+theorem Steps.toStandardForm_halts {p : Program} {s s' : State}
+ (hsteps ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_6db7ce461488_0 | ca80a136088aa3fa | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Total.lean | Total | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "Total.extend_omegaExecution",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let μs : ωSequence Label := .const default\n obtain ⟨ss', ho, h0⟩ := Total.omegaExecution_exists (h := ht) t μ... | [
{
"name": "Total.omegaExecution_exists",
"text": "/-- If a LTS is total, then there exists an infinite execution from any starting state and\nover any infinite sequence of labels. -/\ntheorem Total.omegaExecution_exists [h : lts.Total] (s : State) (μs : ωSequence Label) :\n ∃ ss, lts.OmegaExecution ss μs... | [
{
"name": "Total.extend_omegaExecution",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 527,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Semantics.FLTS.Basic
public import Cslib.Foundations.Semantics.LTS.OmegaExecution
/-!
# Total LTS
This file defines, and ... | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Semantics.FLTS.Basic
public import Cslib.Foundations.Semantics.LTS.OmegaExecution
/-!
# Total LTS
This file defines, and ... | @@ -45,11 +45,21 @@
| 0 => s
| n + 1 => lts.chooseFLTS.tr (lts.chooseOmegaExecution s μs n) (μs n)
+/-- If a LTS is total, then there exists an infinite execution from any starting state and
+over any infinite sequence of labels. -/
+theorem Total.omegaExecution_exists [h : lts.Total] (s : State) (μs : ωSequenc... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_6db7ce461488_1 | 73aced897b47a5a4 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Total.lean | Total | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "totalize.nonsink_mtr_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor <;> intro h\n · generalize h_s : (some s : Option State) = s'\n generalize h_t : (some t : Option... | [
{
"name": "totalize.nonsink_tr_iff",
"text": "/-- In `totalize`, the transitions between non-sink states correspond exactly to\nthe transitions in the original LTS. -/\n@[simp]\ntheorem totalize.nonsink_tr_iff {μ : Label} {s t : State} :\n lts.totalize.Tr (some s) μ (some t) ↔ lts.Tr s μ t := by\n simp ... | [
{
"name": "totalize.nonsink_mtr_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 872,
"n_subproofs": 1,
"n_tactics": 17,
"cyclomatic": 6,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 6,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Semantics.FLTS.Basic
public import Cslib.Foundations.Semantics.LTS.OmegaExecution
/-!
# Total LTS
This file defines, and ... | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Semantics.FLTS.Basic
public import Cslib.Foundations.Semantics.LTS.OmegaExecution
/-!
# Total LTS
This file defines, and ... | @@ -70,14 +70,33 @@
· grind
· grind only [totalize]
+/-- In `totalize`, the transitions between non-sink states correspond exactly to
+the transitions in the original LTS. -/
+@[simp]
+theorem totalize.nonsink_tr_iff {μ : Label} {s t : State} :
+ lts.totalize.Tr (some s) μ (some t) ↔ lts.Tr s μ t := by
+ si... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_0 | 890be6fb1ef217dd | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "cumLen_segment_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h0 : ls.cumLen 0 ≤ n := by simp [cumLen_zero]\n have h1 : n < ls.cumLen 1 := by simpa [cumLen_succ, cumLen_zero]\... | [
{
"name": "cumLen_strictMono",
"text": "/-- If all lists in `ls` are nonempty, then `ls.cumLen` is strictly monotonic. -/\ntheorem cumLen_strictMono {ls : ωSequence (List α)} (h_ls : ∀ k, (ls k).length > 0) :\n StrictMono ls.cumLen := by\n grind [strictMono_nat_of_lt_succ]\n\n",
"fan_in": 2,
"n_... | [
{
"name": "cumLen_segment_zero",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 366,
"n_subproofs": 2,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -51,9 +51,17 @@
ls.cumLen (1 + k) = (ls 0).length + (ls.drop 1).cumLen k := by
induction k <;> grind
+/-- If all lists in `ls` are nonempty, then `ls.cumLen` is strictly monotonic. -/
+theorem cumLen_strictMono {ls : ωSequence (List α)} (h_ls : ∀ k, (ls k).length > 0) :
+ StrictMono ls.cumLen := by
+ g... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_1 | 1763682a43f4499d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "cumLen_segment_one_add",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have h0 : (ls.drop 1).cumLen 0 = 0 := by simp [cumLen_zero]\n rw [add_comm, segment_plus_one h0]; unf... | [
{
"name": "cumLen_one_add_drop",
"text": "theorem cumLen_one_add_drop (ls : ωSequence (List α)) (k : ℕ) :\n ls.cumLen (1 + k) = (ls 0).length + (ls.drop 1).cumLen k := by\n induction k <;> grind\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 3,
"c... | [
{
"name": "cumLen_segment_one_add",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 34,
"n_chars": 1688,
"n_subproofs": 5,
"n_tactics": 37,
"cyclomatic": 10,
"n_automation": 17,
"n_rewrites": 3,
"n_structural": 13,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -47,6 +47,10 @@
ls.cumLen (k + 1) = ls.cumLen k + (ls k).length :=
rfl
+theorem cumLen_one_add_drop (ls : ωSequence (List α)) (k : ℕ) :
+ ls.cumLen (1 + k) = (ls 0).length + (ls.drop 1).cumLen k := by
+ induction k <;> grind
+
/-- If all lists in `ls` are nonempty, then `ls.cumLen` is strictly monoton... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_2 | b130352234357255 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "cons_flatten",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext n; rw [flatten_def, head, tail_eq_drop]\n rcases (show n < (ls 0).length ∨ n ≥ (ls 0).length by omega) with h_n | h_n\n ... | [
{
"name": "flatten_def",
"text": "theorem flatten_def [Inhabited α] (ls : ωSequence (List α)) (n : ℕ) :\n flatten ls n = (ls (segment ls.cumLen n))[n - ls.cumLen (segment ls.cumLen n)]! :=\n rfl\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": 1,
"c... | [
{
"name": "cons_flatten",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 7,
"n_lines": 12,
"n_chars": 586,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nesting":... | 4 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -102,10 +102,20 @@
noncomputable def flatten [Inhabited α] (ls : ωSequence (List α)) : ωSequence α :=
fun n ↦ (ls (segment ls.cumLen n))[n - ls.cumLen (segment ls.cumLen n)]!
+theorem flatten_def [Inhabited α] (ls : ωSequence (List α)) (n : ℕ) :
+ flatten ls n = (ls (segment ls.cumLen n))[n - ls.cumLen (seg... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_3 | 67d4ab080168f7e7 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "flatten_take_drop",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply append_left_right_injective\n · rw [append_flatten h_ls n, append_take_drop (ls.cumLen n) ls.flatten]\n · rw [len... | [
{
"name": "length_flatten_take",
"text": "/-- The length of `(ls.take n).flatten` is `ls.cumLen n`. -/\n@[simp, nolint simpNF, scoped grind =]\ntheorem length_flatten_take {ls : ωSequence (List α)} (n : ℕ) :\n (ls.take n).flatten.length = ls.cumLen n := by\n induction n <;> grind [take_succ']\n\n",
... | [
{
"name": "flatten_take_drop",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 530,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nest... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -123,6 +123,12 @@
(n : ℕ) : (ls.take n).flatten ++ω (ls.drop n).flatten = ls.flatten := by
induction n generalizing ls <;> grind [tail_eq_drop, take_succ]
+/-- The length of `(ls.take n).flatten` is `ls.cumLen n`. -/
+@[simp, nolint simpNF, scoped grind =]
+theorem length_flatten_take {ls : ωSequence (List... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_4 | 7976daf83e5d71f9 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "flatten_take",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (flatten_take_drop h_ls n).1",
"n_chars": 31,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "flatten_take_drop",
"text": "/-- `In fact, (ls.take n).flatten` is `ls.flatten.take (ls.cumLen n)`\nand (ls.drop n).flatten` is `ls.flatten.drop (ls.cumLen n)`. -/\ntheorem flatten_take_drop [Inhabited α]\n {ls : ωSequence (List α)} (h_ls : ∀ k, (ls k).length > 0) (n : ℕ) :\n (ls.take n).fl... | [
{
"name": "flatten_take",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 205,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": ... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -129,13 +129,25 @@
(ls.take n).flatten.length = ls.cumLen n := by
induction n <;> grind [take_succ']
+/-- `In fact, (ls.take n).flatten` is `ls.flatten.take (ls.cumLen n)`
+and (ls.drop n).flatten` is `ls.flatten.drop (ls.cumLen n)`. -/
+theorem flatten_take_drop [Inhabited α]
+ {ls : ωSequence (List α)... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_5 | e05f0bd83d7876e3 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "extract_flatten",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_ls' : ∀ k, (ls.drop n k).length > 0 := by grind\n have h_drop := flatten_drop h_ls n\n have h_take := flatten_take... | [
{
"name": "flatten_take",
"text": "theorem flatten_take [Inhabited α]\n {ls : ωSequence (List α)} (h_ls : ∀ k, (ls k).length > 0) (n : ℕ) :\n (ls.take n).flatten = ls.flatten.take (ls.cumLen n) :=\n (flatten_take_drop h_ls n).1\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 205,
"n_subpr... | [
{
"name": "extract_flatten",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 11,
"n_chars": 482,
"n_subproofs": 3,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 5 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -139,6 +139,11 @@
· rw [append_flatten h_ls n, append_take_drop (ls.cumLen n) ls.flatten]
· rw [length_flatten_take, length_take]
+theorem flatten_take [Inhabited α]
+ {ls : ωSequence (List α)} (h_ls : ∀ k, (ls k).length > 0) (n : ℕ) :
+ (ls.take n).flatten = ls.flatten.take (ls.cumLen n) :=
+ (flatte... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_6 | 4bbcc34feae58b23 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "flatten_take",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (flatten_take_drop h_ls n).1",
"n_chars": 31,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "flatten_take_drop",
"text": "/-- `In fact, (ls.take n).flatten` is `ls.flatten.take (ls.cumLen n)`\nand (ls.drop n).flatten` is `ls.flatten.drop (ls.cumLen n)`. -/\ntheorem flatten_take_drop [Inhabited α]\n {ls : ωSequence (List α)} (h_ls : ∀ k, (ls k).length > 0) (n : ℕ) :\n (ls.take n).fl... | [
{
"name": "forall_flatten_iff",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 10,
"n_chars": 471,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nes... | 8 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -129,13 +129,25 @@
(ls.take n).flatten.length = ls.cumLen n := by
induction n <;> grind [take_succ']
+/-- `In fact, (ls.take n).flatten` is `ls.flatten.take (ls.cumLen n)`
+and (ls.drop n).flatten` is `ls.flatten.drop (ls.cumLen n)`. -/
+theorem flatten_take_drop [Inhabited α]
+ {ls : ωSequence (List α)... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_e95dd66f1bee_7 | 6fe15a1fe43d0eb4 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/OmegaSequence/Flatten.lean | Flatten | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "segment_toSegs_cumLen",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext n\n have (n' : ℕ) := hm (show n' < n' + 1 by omega)\n induction n <;> grind [toSegs_def]",
"n_chars": 100,
... | [
{
"name": "toSegs_def",
"text": "theorem toSegs_def (s : ωSequence α) (f : ℕ → ℕ) (n : ℕ) :\n s.toSegs f n = s.extract (f n) (f (n + 1)) :=\n rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 126,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewr... | [
{
"name": "segment_toSegs_cumLen",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 293,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Foundations.Data.Nat.Segment
public import Cslib.Foundations.Data.OmegaSequence.Init
/-!
# Flattening an infinite sequence of lists
G... | @@ -165,17 +165,28 @@
def toSegs (s : ωSequence α) (f : ℕ → ℕ) : ωSequence (List α) :=
fun n ↦ s.extract (f n) (f (n + 1))
+theorem toSegs_def (s : ωSequence α) (f : ℕ → ℕ) (n : ℕ) :
+ s.toSegs f n = s.extract (f n) (f (n + 1)) :=
+ rfl
+
/-- `(s.toSegs f).cumLen` is `f` itself. -/
@[simp]
theorem segment_... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_457ba5f5e459_0 | 7fc51803b9b94045 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Automata/DA/Congr.lean | Congr | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "congr_language_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext\n #adaptation_note\n /-- A grind regression found moving to nightly-2026-03-31 (changes from lean#13166) -/\n cons... | [
{
"name": "congr_mtr_eq",
"text": "/-- After consuming a finite word `xs`, `c.toDA` reaches the state `⟦ xs ⟧` which is\nthe equivalence class of `xs`. -/\n@[simp, scoped grind =]\ntheorem congr_mtr_eq {xs : List Symbol} :\n c.toDA.mtr c.toDA.start xs = ⟦ xs ⟧ := by\n generalize h_rev : xs.reverse = ys\... | [
{
"name": "congr_language_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 429,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.DA.Basic
public import Cslib.Computability.Languages.Congruences.RightCongruence
/-! # Deterministic automaton ... | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.DA.Basic
public import Cslib.Computability.Languages.Congruences.RightCongruence
/-! # Deterministic automaton ... | @@ -36,6 +36,19 @@
variable [c : RightCongruence Symbol]
+/-- After consuming a finite word `xs`, `c.toDA` reaches the state `⟦ xs ⟧` which is
+the equivalence class of `xs`. -/
+@[simp, scoped grind =]
+theorem congr_mtr_eq {xs : List Symbol} :
+ c.toDA.mtr c.toDA.start xs = ⟦ xs ⟧ := by
+ generalize h_rev : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_54a45d9eece7_0 | 635e672d405ebc81 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Logics/Modal/Cube.lean | Cube | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "k_subset_t",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n K World Atom ⊆ D World Atom := k_subset_d\n D World Atom ⊆ T World Atom := d_subset_t",
"n_chars": 106,
"n_... | [
{
"name": "k_subset_d",
"text": "theorem k_subset_d : K World Atom ⊆ D World Atom := by\n grind only [subset_def, D, K, = setOf_true, = logic, mem_setOf_eq, = Proposition.valid]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 148,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"... | [
{
"name": "k_subset_t",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 4
... | 1 | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Marianna Girlando
-/
module
public import Cslib.Logics.Modal.Basic
/-! # Modal Logic Cube
This module formalises the Modal Cube, including all the 15 foundation... | /-
Copyright (c) 2026 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Marianna Girlando
-/
module
public import Cslib.Logics.Modal.Basic
/-! # Modal Logic Cube
This module formalises the Modal Cube, including all the 15 foundation... | @@ -96,11 +96,17 @@
open scoped Proposition
open Set
+theorem k_subset_d : K World Atom ⊆ D World Atom := by
+ grind only [subset_def, D, K, = setOf_true, = logic, mem_setOf_eq, = Proposition.valid]
+
open scoped Relation in
theorem d_subset_t : D World Atom ⊆ T World Atom := by
grind
-theorem k_subset_t : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9ae04259b66c_0 | a81e917b2e0abf42 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Automata/NA/BuchiInter.lean | BuchiInter | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "inter_language_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply mem_ext\n intro xs\n simp only [ωLanguage.mem_iInf]\n constructor\n · intro ⟨ss, h_run, h_inf⟩ i\n use ss.m... | [
{
"name": "inter_freq_comp_acc_freq_acc",
"text": "/-- If the intersection automaton sees the accepting conditions of both component automata\ninfinitely many times, then its own accepting condition also happens infinitely many times. -/\nlemma inter_freq_comp_acc_freq_acc {xs : ωSequence Symbol} {ss : ωSeq... | [
{
"name": "inter_language_eq",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 38,
"n_chars": 1363,
"n_subproofs": 3,
"n_tactics": 34,
"cyclomatic": 6,
"n_automation": 10,
"n_rewrites": 0,
"n_structural": 20,
"automation_only": false,
"max_... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Hist
public import Cslib.Computability.Automata.NA.Prod
public import Cslib.Foundations.Data.OmegaSequence.Te... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Hist
public import Cslib.Computability.Automata.NA.Prod
public import Cslib.Foundations.Data.OmegaSequence.Te... | @@ -76,6 +76,23 @@
· apply Frequently.mono h_inf
grind
+/-- If the intersection automaton sees the accepting conditions of both component automata
+infinitely many times, then its own accepting condition also happens infinitely many times. -/
+lemma inter_freq_comp_acc_freq_acc {xs : ωSequence Symbol} {ss... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_423cc48218cc_0 | 757c355abd93dd43 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/PerfectSecrecy/Internal/PerfectSecrecy.lean | PerfectSecrecy | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "perfectlySecret_iff_indep",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h msgDist m c\n by_cases hc : (scheme.marginalCiphertextDist msgDist) c = 0\n · hav... | [
{
"name": "jointDist_tsum_fst",
"text": "/-- Summing the joint distribution over messages gives the marginal ciphertext distribution. -/\ntheorem jointDist_tsum_fst (scheme : EncScheme M K C) (msgDist : PMF M) (c : C) :\n ∑' m, scheme.jointDist msgDist (m, c) = scheme.marginalCiphertextDist msgDist c :=\... | [
{
"name": "perfectlySecret_iff_indep",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 25,
"n_chars": 1177,
"n_subproofs": 3,
"n_tactics": 18,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | @@ -28,6 +28,11 @@
universe u
variable {M K C : Type u}
+/-- Summing the joint distribution over messages gives the marginal ciphertext distribution. -/
+theorem jointDist_tsum_fst (scheme : EncScheme M K C) (msgDist : PMF M) (c : C) :
+ ∑' m, scheme.jointDist msgDist (m, c) = scheme.marginalCiphertextDist msgDi... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_423cc48218cc_1 | 2e73aef86737ca62 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/PerfectSecrecy/Internal/PerfectSecrecy.lean | PerfectSecrecy | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "indep_of_ciphertextIndist",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [jointDist_eq]; congr 1\n change scheme.ciphertextDist m c =\n PMF.bind msgDist (fun m' => scheme.cipherte... | [
{
"name": "jointDist_eq",
"text": "/-- The joint distribution at `(m, c)` equals `msgDist m * ciphertextDist m c`. -/\ntheorem jointDist_eq (scheme : EncScheme M K C) (msgDist : PMF M)\n (m : M) (c : C) :\n scheme.jointDist msgDist (m, c) = msgDist m * scheme.ciphertextDist m c :=\n Cslib.Probability... | [
{
"name": "indep_of_ciphertextIndist",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 560,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 6,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | @@ -28,12 +28,24 @@
universe u
variable {M K C : Type u}
+/-- The joint distribution at `(m, c)` equals `msgDist m * ciphertextDist m c`. -/
+theorem jointDist_eq (scheme : EncScheme M K C) (msgDist : PMF M)
+ (m : M) (c : C) :
+ scheme.jointDist msgDist (m, c) = msgDist m * scheme.ciphertextDist m c :=
+ Cs... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_423cc48218cc_2 | 154e0cfa1ff08fd4 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/PerfectSecrecy/Internal/PerfectSecrecy.lean | PerfectSecrecy | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "perfectlySecret_of_ciphertextIndist",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (perfectlySecret_iff_indep scheme).mpr (fun msgDist m c =>\n indep_of_ciphertextIndist scheme h msgDist... | [
{
"name": "perfectlySecret_iff_indep",
"text": "/-- Perfect secrecy is equivalent to message-ciphertext independence.\nThe two formulations are related by multiplying/dividing by `marginal(c)`. -/\ntheorem perfectlySecret_iff_indep (scheme : EncScheme M K C) :\n scheme.PerfectlySecret ↔\n ∀ (msgDist :... | [
{
"name": "perfectlySecret_of_ciphertextIndist",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 315,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fal... | 4 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | @@ -39,6 +39,30 @@
∑' m, scheme.jointDist msgDist (m, c) = scheme.marginalCiphertextDist msgDist c :=
Cslib.Probability.PMF.bind_pair_tsum_fst msgDist scheme.ciphertextDist c
+/-- Perfect secrecy is equivalent to message-ciphertext independence.
+The two formulations are related by multiplying/dividing by `ma... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_423cc48218cc_3 | bea3d362645f09b2 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/PerfectSecrecy/Internal/PerfectSecrecy.lean | PerfectSecrecy | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "perfectlySecret_of_ciphertextIndist",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (perfectlySecret_iff_indep scheme).mpr (fun msgDist m c =>\n indep_of_ciphertextIndist scheme h msgDist... | [
{
"name": "perfectlySecret_iff_indep",
"text": "/-- Perfect secrecy is equivalent to message-ciphertext independence.\nThe two formulations are related by multiplying/dividing by `marginal(c)`. -/\ntheorem perfectlySecret_iff_indep (scheme : EncScheme M K C) :\n scheme.PerfectlySecret ↔\n ∀ (msgDist :... | [
{
"name": "ciphertextIndist_of_perfectlySecret",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 832,
"n_subproofs": 4,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 6,
"automation_only": f... | 3 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | @@ -39,10 +39,46 @@
∑' m, scheme.jointDist msgDist (m, c) = scheme.marginalCiphertextDist msgDist c :=
Cslib.Probability.PMF.bind_pair_tsum_fst msgDist scheme.ciphertextDist c
+/-- Perfect secrecy is equivalent to message-ciphertext independence.
+The two formulations are related by multiplying/dividing by `m... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_423cc48218cc_4 | ff5682f3db9831cc | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/PerfectSecrecy/Internal/PerfectSecrecy.lean | PerfectSecrecy | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "perfectlySecret_of_ciphertextIndist",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (perfectlySecret_iff_indep scheme).mpr (fun msgDist m c =>\n indep_of_ciphertextIndist scheme h msgDist... | [
{
"name": "perfectlySecret_iff_indep",
"text": "/-- Perfect secrecy is equivalent to message-ciphertext independence.\nThe two formulations are related by multiplying/dividing by `marginal(c)`. -/\ntheorem perfectlySecret_iff_indep (scheme : EncScheme M K C) :\n scheme.PerfectlySecret ↔\n ∀ (msgDist :... | [
{
"name": "shannonKeySpace",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 18,
"n_chars": 809,
"n_subproofs": 4,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 6,
"automation_only": false,
"max_nesti... | 5 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Crypto.Protocols.PerfectSecrecy.Defs
public import Mathlib.Probability.Distributions.Uniform
/-!
# Perfect Secrecy: Internal pro... | @@ -39,10 +39,46 @@
∑' m, scheme.jointDist msgDist (m, c) = scheme.marginalCiphertextDist msgDist c :=
Cslib.Probability.PMF.bind_pair_tsum_fst msgDist scheme.ciphertextDist c
+/-- Perfect secrecy is equivalent to message-ciphertext independence.
+The two formulations are related by multiplying/dividing by `m... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_3f76754a5a5e_0 | dfa6c53cabd1b3d7 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/StackTape.lean | StackTape | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "cons_head_tail",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff]\n simp",
"n_chars": 24,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": ... | [
{
"name": "eq_iff",
"text": "lemma eq_iff (l1 l2 : StackTape Symbol) :\n l1 = l2 ↔ l1.head = l2.head ∧ l1.tail = l2.tail := by\n constructor\n · grind\n · intro ⟨hhead, htail⟩\n cases l1 with | mk as1 h1 =>\n cases l2 with | mk as2 h2 =>\n cases as1 <;> cases as2 <;> grind [nil]\n\n",
"fa... | [
{
"name": "cons_head_tail",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 113,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2026 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Cslib.Init
/-!
# StackTape: Infinite, eventually-`none` lists of `Option`s
This file defines `StackTape`, a stack-like data structure of `Optio... | /-
Copyright (c) 2026 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Cslib.Init
/-!
# StackTape: Infinite, eventually-`none` lists of `Option`s
This file defines `StackTape`, a stack-like data structure of `Optio... | @@ -105,6 +105,15 @@
| [] => none
| h :: _ => h
+lemma eq_iff (l1 l2 : StackTape Symbol) :
+ l1 = l2 ↔ l1.head = l2.head ∧ l1.tail = l2.tail := by
+ constructor
+ · grind
+ · intro ⟨hhead, htail⟩
+ cases l1 with | mk as1 h1 =>
+ cases l2 with | mk as2 h2 =>
+ cases as1 <;> cases as2 <;> grind [ni... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_dda6caf7f461_0 | 95911763c224903f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/StraightLine.lean | StraightLine | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "straight_line_halts_from_regs",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices h : ∀ s : State, s.pc ≤ p.length → ∃ s', Steps p s s' ∧ s'.pc = p.length by\n obtain ⟨s', hsteps... | [
{
"name": "Step.of_nonJump",
"text": "/-- A non-jumping instruction produces a step that increments PC by 1. -/\ntheorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)\n (hnonjump : ¬(p[s.pc]'hlt).IsJump) :\n ∃ s', Step p s s' ∧ s'.pc = s.pc + 1 := by\n cases hp : (p[s.pc]'hlt) wit... | [
{
"name": "straight_line_halts_from_regs",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 932,
"n_subproofs": 4,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | @@ -36,11 +36,39 @@
instance (p : Program) : Decidable p.IsStraightLine :=
inferInstanceAs (Decidable (∀ i ∈ p, ¬i.IsJump))
+/-- A non-jumping instruction produces a step that increments PC by 1. -/
+theorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)
+ (hnonjump : ¬(p[s.pc]'hlt).IsJump) ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_dda6caf7f461_1 | 65c38d48a47e6b24 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/StraightLine.lean | StraightLine | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "straight_line_halts_from_regs",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices h : ∀ s : State, s.pc ≤ p.length → ∃ s', Steps p s s' ∧ s'.pc = p.length by\n obtain ⟨s', hsteps... | [
{
"name": "Step.of_nonJump",
"text": "/-- A non-jumping instruction produces a step that increments PC by 1. -/\ntheorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)\n (hnonjump : ¬(p[s.pc]'hlt).IsJump) :\n ∃ s', Step p s s' ∧ s'.pc = s.pc + 1 := by\n cases hp : (p[s.pc]'hlt) wit... | [
{
"name": "straight_line_halts",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 296,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | @@ -36,11 +36,39 @@
instance (p : Program) : Decidable p.IsStraightLine :=
inferInstanceAs (Decidable (∀ i ∈ p, ¬i.IsJump))
+/-- A non-jumping instruction produces a step that increments PC by 1. -/
+theorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)
+ (hnonjump : ¬(p[s.pc]'hlt).IsJump) ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_dda6caf7f461_2 | d0fc638d8915a018 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/StraightLine.lean | StraightLine | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "straight_line_halts_from_regs",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices h : ∀ s : State, s.pc ≤ p.length → ∃ s', Steps p s s' ∧ s'.pc = p.length by\n obtain ⟨s', hsteps... | [
{
"name": "Step.of_nonJump",
"text": "/-- A non-jumping instruction produces a step that increments PC by 1. -/\ntheorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)\n (hnonjump : ¬(p[s.pc]'hlt).IsJump) :\n ∃ s', Step p s s' ∧ s'.pc = s.pc + 1 := by\n cases hp : (p[s.pc]'hlt) wit... | [
{
"name": "straightLinefinalState_spec",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 368,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | @@ -36,11 +36,39 @@
instance (p : Program) : Decidable p.IsStraightLine :=
inferInstanceAs (Decidable (∀ i ∈ p, ¬i.IsJump))
+/-- A non-jumping instruction produces a step that increments PC by 1. -/
+theorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)
+ (hnonjump : ¬(p[s.pc]'hlt).IsJump) ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_dda6caf7f461_3 | 0e7fd8b8272d80fc | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/StraightLine.lean | StraightLine | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "straightLineFinalRegs_eq_of_halted",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Steps.eq_of_halts hsteps hhalted (straightLinefinalState_spec hsl r).1\n (straightLinefinalState_spec hs... | [
{
"name": "straightLinefinalState_spec",
"text": "/-- Specification: the state from straightLinefinalState satisfies Steps, isHalted,\nand has pc = p.length. -/\ntheorem straightLinefinalState_spec {p : Program} (hsl : p.IsStraightLine) (r : Regs) :\n let s := straightLinefinalState hsl r\n Steps p ⟨0... | [
{
"name": "straightLineFinalRegs_eq_of_halted",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 428,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true... | 2 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | @@ -76,6 +76,13 @@
(hsl : p.IsStraightLine) (r : Regs) : State :=
Classical.choose (straight_line_halts_from_regs hsl r)
+/-- Specification: the state from straightLinefinalState satisfies Steps, isHalted,
+and has pc = p.length. -/
+theorem straightLinefinalState_spec {p : Program} (hsl : p.IsStraightLine) (... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_dda6caf7f461_4 | 4995d1340aaa90db | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/StraightLine.lean | StraightLine | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "straight_line_halts_from_regs",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices h : ∀ s : State, s.pc ≤ p.length → ∃ s', Steps p s s' ∧ s'.pc = p.length by\n obtain ⟨s', hsteps... | [
{
"name": "Step.of_nonJump",
"text": "/-- A non-jumping instruction produces a step that increments PC by 1. -/\ntheorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)\n (hnonjump : ¬(p[s.pc]'hlt).IsJump) :\n ∃ s', Step p s s' ∧ s'.pc = s.pc + 1 := by\n cases hp : (p[s.pc]'hlt) wit... | [
{
"name": "straight_line_state_at_pc",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 510,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Basic
public import Cslib.Computability.URM.Execution
/-! # Straight-Line Programs
This file defines straight-line programs ... | @@ -36,11 +36,39 @@
instance (p : Program) : Decidable p.IsStraightLine :=
inferInstanceAs (Decidable (∀ i ∈ p, ¬i.IsJump))
+/-- A non-jumping instruction produces a step that increments PC by 1. -/
+theorem Step.of_nonJump {p : Program} {s : State} (hlt : s.pc < p.length)
+ (hnonjump : ¬(p[s.pc]'hlt).IsJump) ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2b018ac879d7_4 | 5ed19a72c81a449b | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Evaluation.lean | Evaluation | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "redexFree_iff_mred_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n case mp => grind [RedexFree.normal_red]\n case mpr =>\n intro h\n rw [redexFree_iff]\n intro... | [
{
"name": "redexFree_iff",
"text": "/-- A term is redex free iff it has no one-step reductions. -/\ntheorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal Red x :=\n ⟨RedexFree.normal_red, redexFree_of_normal_red⟩\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 184,
"n_subproofs": 0,
"n_tac... | [
{
"name": "unique_normal_form",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 8,
"n_chars": 298,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nest... | 5 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | @@ -147,6 +147,10 @@
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨hx, _⟩, _ ⬝ _, red_head _ _ _ hq => exact hx.normal_red ⟨_, hq⟩
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨_, hy⟩, _ ⬝ _, red_tail _ _ _ he => exact hy.normal_red ⟨_, he⟩
+/-- A term is redex free iff it has no one-step reductions. -/
+theorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2b018ac879d7_5 | a13d6208fe2b0438 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Evaluation.lean | Evaluation | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "redexFree_iff_mred_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n case mp => grind [RedexFree.normal_red]\n case mpr =>\n intro h\n rw [redexFree_iff]\n intro... | [
{
"name": "redexFree_iff",
"text": "/-- A term is redex free iff it has no one-step reductions. -/\ntheorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal Red x :=\n ⟨RedexFree.normal_red, redexFree_of_normal_red⟩\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 184,
"n_subproofs": 0,
"n_tac... | [
{
"name": "eq_of_mJoin_red_redexFree",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 8,
"n_chars": 298,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"m... | 5 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | @@ -147,6 +147,10 @@
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨hx, _⟩, _ ⬝ _, red_head _ _ _ hq => exact hx.normal_red ⟨_, hq⟩
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨_, hy⟩, _ ⬝ _, red_tail _ _ _ he => exact hy.normal_red ⟨_, he⟩
+/-- A term is redex free iff it has no one-step reductions. -/
+theorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2b018ac879d7_7 | af3e0b2373f51997 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Evaluation.lean | Evaluation | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "redexFree_iff_mred_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n case mp => grind [RedexFree.normal_red]\n case mpr =>\n intro h\n rw [redexFree_iff]\n intro... | [
{
"name": "redexFree_iff",
"text": "/-- A term is redex free iff it has no one-step reductions. -/\ntheorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal Red x :=\n ⟨RedexFree.normal_red, redexFree_of_normal_red⟩\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 184,
"n_subproofs": 0,
"n_tac... | [
{
"name": "isBool_injective",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 15,
"n_chars": 607,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": false,
"max_nest... | 5 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | @@ -147,6 +147,10 @@
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨hx, _⟩, _ ⬝ _, red_head _ _ _ hq => exact hx.normal_red ⟨_, hq⟩
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨_, hy⟩, _ ⬝ _, red_tail _ _ _ he => exact hy.normal_red ⟨_, he⟩
+/-- A term is redex free iff it has no one-step reductions. -/
+theorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2b018ac879d7_8 | 56f468db1b52fb60 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Evaluation.lean | Evaluation | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "redexFree_iff_mred_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n case mp => grind [RedexFree.normal_red]\n case mpr =>\n intro h\n rw [redexFree_iff]\n intro... | [
{
"name": "redexFree_iff",
"text": "/-- A term is redex free iff it has no one-step reductions. -/\ntheorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal Red x :=\n ⟨RedexFree.normal_red, redexFree_of_normal_red⟩\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 184,
"n_subproofs": 0,
"n_tac... | [
{
"name": "TF_nequiv",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 4,
"n_chars": 140,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 6 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | @@ -147,6 +147,10 @@
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨hx, _⟩, _ ⬝ _, red_head _ _ _ hq => exact hx.normal_red ⟨_, hq⟩
| _ ⬝ _ ⬝ _ ⬝ _ ⬝ _, ⟨_, hy⟩, _ ⬝ _, red_tail _ _ _ he => exact hy.normal_red ⟨_, he⟩
+/-- A term is redex free iff it has no one-step reductions. -/
+theorem redexFree_iff {x : SKI} : x.RedexFree ↔ Normal... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2b018ac879d7_9 | b08bd2abc72bbcf1 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Evaluation.lean | Evaluation | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "mJoin_red_redexFree",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n let ⟨w, hyw, hzw⟩ := h\n (redexFree_iff_mred_eq.1 hy _ |>.1 hzw : y = w) ▸ hyw",
"n_chars": 87,
"n_subproofs": 0,... | [
{
"name": "redexFree_iff_mred_eq",
"text": "/-- A term is redex free iff its only many-step reduction is itself. -/\ntheorem redexFree_iff_mred_eq {x : SKI} : x.RedexFree ↔ ∀ y, (x ↠ y) ↔ x = y := by\n constructor\n case mp => grind [RedexFree.normal_red]\n case mpr =>\n intro h\n rw [redexFree_iff... | [
{
"name": "isChurch_injective",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 15,
"n_chars": 687,
"n_subproofs": 1,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": false,
"max_ne... | 7 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | @@ -166,12 +166,26 @@
instance : DecidablePred RedexFree := fun _ => decidable_of_iff' _ redexFree_iff_evalStep
+/-- A term is redex free iff its only many-step reduction is itself. -/
+theorem redexFree_iff_mred_eq {x : SKI} : x.RedexFree ↔ ∀ y, (x ↠ y) ↔ x = y := by
+ constructor
+ case mp => grind [RedexFree.... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2b018ac879d7_10 | 8a06cb2c04267137 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Evaluation.lean | Evaluation | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "mJoin_red_redexFree",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n let ⟨w, hyw, hzw⟩ := h\n (redexFree_iff_mred_eq.1 hy _ |>.1 hzw : y = w) ▸ hyw",
"n_chars": 87,
"n_subproofs": 0,... | [
{
"name": "redexFree_iff_mred_eq",
"text": "/-- A term is redex free iff its only many-step reduction is itself. -/\ntheorem redexFree_iff_mred_eq {x : SKI} : x.RedexFree ↔ ∀ y, (x ↠ y) ↔ x = y := by\n constructor\n case mp => grind [RedexFree.normal_red]\n case mpr =>\n intro h\n rw [redexFree_iff... | [
{
"name": "rice",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 36,
"n_chars": 1856,
"n_subproofs": 5,
"n_tactics": 36,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 27,
"automation_only": false,
"max_nesting": 6
... | 7 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | @@ -166,8 +166,24 @@
instance : DecidablePred RedexFree := fun _ => decidable_of_iff' _ redexFree_iff_evalStep
-lemma sk_nequiv : ¬ MJoin Red S K := sorry
+/-- A term is redex free iff its only many-step reduction is itself. -/
+theorem redexFree_iff_mred_eq {x : SKI} : x.RedexFree ↔ ∀ y, (x ↠ y) ↔ x = y := by
+ ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2b018ac879d7_11 | 61942203009d47fc | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Evaluation.lean | Evaluation | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 5 | [
{
"theorem_name": "mJoin_red_redexFree",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n let ⟨w, hyw, hzw⟩ := h\n (redexFree_iff_mred_eq.1 hy _ |>.1 hzw : y = w) ▸ hyw",
"n_chars": 87,
"n_subproofs": 0,... | [
{
"name": "redexFree_iff_mred_eq",
"text": "/-- A term is redex free iff its only many-step reduction is itself. -/\ntheorem redexFree_iff_mred_eq {x : SKI} : x.RedexFree ↔ ∀ y, (x ↠ y) ↔ x = y := by\n constructor\n case mp => grind [RedexFree.normal_red]\n case mpr =>\n intro h\n rw [redexFree_iff... | [
{
"name": "rice'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 12,
"n_chars": 554,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2
}
... | 8 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Confluence
public import Cslib.Languages.CombinatoryLogic.Recursion
/-!
# Evaluation results
This file formali... | @@ -166,8 +166,24 @@
instance : DecidablePred RedexFree := fun _ => decidable_of_iff' _ redexFree_iff_evalStep
-lemma sk_nequiv : ¬ MJoin Red S K := sorry
+/-- A term is redex free iff its only many-step reduction is itself. -/
+theorem redexFree_iff_mred_eq {x : SKI} : x.RedexFree ↔ ∀ y, (x ↠ y) ↔ x = y := by
+ ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_014ca8527022_0 | 861ffa033ee20709 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StandardReduction.lean | StandardReduction | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "Standard.of_cbn",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n cbn_trans step (lc_refl N lc_N)",
"n_chars": 34,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "Standard.cbn_trans",
"text": "/-- A Call-by-Name reduction followed by a standard reduction is a standard reduction. -/\nlemma Standard.cbn_trans (h1 : M ↠ₙ P) (h2 : P ⭢ₛ N) : M ⭢ₛ N := by\n induction h1 with\n | refl => exact h2\n | tail _ h_step ih => exact ih (cbn_step_trans h_step h2)\n\n"... | [
{
"name": "Standard.trans_step",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 989,
"n_subproofs": 4,
"n_tactics": 20,
"cyclomatic": 5,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.CallByName
/-! # Standard Reduction and the Standardization T... | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.CallByName
/-! # Standard Reduction and the Standardization T... | @@ -66,6 +66,12 @@
| app std_L' std_M => exact app (ih std_L') std_M
| rdx _ lc_Z cbn_m std_body => exact rdx step_M.lc_l lc_Z (.head step_M cbn_m) std_body
+/-- A Call-by-Name reduction followed by a standard reduction is a standard reduction. -/
+lemma Standard.cbn_trans (h1 : M ↠ₙ P) (h2 : P ⭢ₛ N) : M ⭢ₛ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2d7ad8279ebb_0 | c57d67ec98fd228c | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/MyhillNerode.lean | MyhillNerode | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "IsRegular.finite_nerodeQuotient",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨State, hFin, M, hM⟩ := IsRegular.iff_dfa.mp h\n rw [← hM]\n apply Finite.of_surjective (fun s ↦ ... | [
{
"name": "da_nerodeCongruence_iff",
"text": "/-- The statement (two strings are related by the Nerode congruence `c_l` on `l` iff all their right\nextensions are either both in the language or both not in it) is equivalent to stating that (all\ntheir right extensions are either both accepted or rejected by... | [
{
"name": "IsRegular.finite_nerodeQuotient",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 633,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 6,
"automation_only": false... | 1 | /-
Copyright (c) 2026 Akhilesh Balaji. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Akhilesh Balaji, Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.RegularLanguage
public import Mathlib.SetTheory.Cardinal.NatCard
/-! # Myhill-Nerode Theorem
... | /-
Copyright (c) 2026 Akhilesh Balaji. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Akhilesh Balaji, Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.RegularLanguage
public import Mathlib.SetTheory.Cardinal.NatCard
/-! # Myhill-Nerode Theorem
... | @@ -83,6 +83,15 @@
· intro hx
use x, hx
+/-- The statement (two strings are related by the Nerode congruence `c_l` on `l` iff all their right
+extensions are either both in the language or both not in it) is equivalent to stating that (all
+their right extensions are either both accepted or rejected by the DF... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
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