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_b114d31242b6_5 | 5df8e794adddc8c2 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "by_axm!",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " Entailment.by_axm (by simpa)",
"n_chars": 29,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
... | [
{
"name": "by_axm",
"text": "lemma by_axm [DecidableEq F] {Γ : Set F} {φ : F} (h : φ ∈ Γ) : Γ *⊢[𝓢] φ := Axiomatized.provable_refl _ (by simpa)\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 129,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites"... | [
{
"name": "by_axm!",
"fan_in": 4,
"n_deps_direct": 4,
"n_deps_transitive": 2,
"n_lines": 3,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 1
}
] | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -595,6 +595,8 @@
def byAxm [DecidableEq F] {Γ : Set F} {φ : F} (h : φ ∈ Γ) : Γ *⊢[𝓢]! φ := Axiomatized.prfAxm (by simpa)
+lemma by_axm [DecidableEq F] {Γ : Set F} {φ : F} (h : φ ∈ Γ) : Γ *⊢[𝓢] φ := Axiomatized.provable_refl _ (by simpa)
+
instance : Compact (Context F 𝓢) where
core := fun b ↦ AdjunctiveS... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_6 | ed7f94e1f237638c | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 8 | [
{
"theorem_name": "CONV!",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " deduct'! NO!",
"n_chars": 13,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0... | [
{
"name": "deduct'!",
"text": "lemma deduct'! (h : [φ] ⊢[𝓢] ψ) : 𝓢 ⊢ φ 🡒 ψ := ⟨FiniteContext.deduct' h.some⟩\n\n\n",
"fan_in": 8,
"n_lines": 4,
"n_chars": 101,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
... | [
{
"name": "CONV!",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 3,
"n_chars": 64,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1
}
] | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -496,6 +496,8 @@
def deduct' : [φ] ⊢[𝓢]! ψ → 𝓢 ⊢! φ 🡒 ψ := fun b ↦ emptyPrf <| deduct b
+lemma deduct'! (h : [φ] ⊢[𝓢] ψ) : 𝓢 ⊢ φ 🡒 ψ := ⟨FiniteContext.deduct' h.some⟩
+
def deductInv' : 𝓢 ⊢! φ 🡒 ψ → [φ] ⊢[𝓢]! ψ := fun b ↦ deductInv <| of b
instance deduction : Deduction (FiniteContext F 𝓢) where
@... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_7 | a770c05df970eae4 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "left_K!_intro_right",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply CK!_iff_CC!.mpr;\n apply deduct'!;\n exact FiniteContext.of'! (Γ := [ψ]) h;",
"n_chars": 89,
"n_subproo... | [
{
"name": "of'!",
"text": "lemma of'! [DecidableEq F] (h : 𝓢 ⊢ φ) : Γ ⊢[𝓢] φ := weakening! (by simp) $ provable_iff_provable.mp h\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 117,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_s... | [
{
"name": "left_K!_intro_right",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 11,
"n_lines": 7,
"n_chars": 193,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_ne... | 4 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -455,6 +455,8 @@
def provable_iff_provable {φ : F} : 𝓢 ⊢ φ ↔ [] ⊢[𝓢] φ :=
⟨fun b ↦ ⟨of b.some⟩, fun b ↦ ⟨emptyPrf b.some⟩⟩
+lemma of'! [DecidableEq F] (h : 𝓢 ⊢ φ) : Γ ⊢[𝓢] φ := weakening! (by simp) $ provable_iff_provable.mp h
+
def id : [φ] ⊢[𝓢]! φ := nthAxm 0
@[simp] lemma id! : [φ] ⊢[𝓢] φ := nth_axm... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_8 | 7f2fdb88d62b6e22 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "cut!",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply deduct'!;\n exact of_C!_of_C!_of_A! (right_A!_intro_left $ of'! (CK!_iff_CC!.mp d₁) ⨀ (K!_left id!)) or₂! (of'! d₂ ⨀ K!_right i... | [
{
"name": "of_C!_of_C!_of_A!",
"text": "lemma of_C!_of_C!_of_A! [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢ φ 🡒 χ) (d₂ : 𝓢 ⊢ ψ 🡒 χ) (d₃ : 𝓢 ⊢ φ ⋎ ψ) : 𝓢 ⊢ χ := ⟨of_C_of_C_of_A d₁.some d₂.some d₃.some⟩\nalias A!_cases := of_C!_of_C!_of_A!\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 256,
... | [
{
"name": "cut!",
"fan_in": 0,
"n_deps_direct": 9,
"n_deps_transitive": 16,
"n_lines": 6,
"n_chars": 315,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2
}
] | 7 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -140,6 +140,9 @@
def of_C_of_C_of_A [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢! φ 🡒 χ) (d₂ : 𝓢 ⊢! ψ 🡒 χ) (d₃ : 𝓢 ⊢! φ ⋎ ψ) : 𝓢 ⊢! χ := or₃ ⨀ d₁ ⨀ d₂ ⨀ d₃
alias A_cases := of_C_of_C_of_A
+lemma of_C!_of_C!_of_A! [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢ φ 🡒 χ) (d₂ : 𝓢 ⊢ ψ 🡒 χ) (d₃ : 𝓢 ⊢ φ ⋎ ψ)... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_9 | fc1b7ac447618b5f | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "cut!",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply deduct'!;\n exact of_C!_of_C!_of_A! (right_A!_intro_left $ of'! (CK!_iff_CC!.mp d₁) ⨀ (K!_left id!)) or₂! (of'! d₂ ⨀ K!_right i... | [
{
"name": "of_C!_of_C!_of_A!",
"text": "lemma of_C!_of_C!_of_A! [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢ φ 🡒 χ) (d₂ : 𝓢 ⊢ ψ 🡒 χ) (d₃ : 𝓢 ⊢ φ ⋎ ψ) : 𝓢 ⊢ χ := ⟨of_C_of_C_of_A d₁.some d₂.some d₃.some⟩\nalias A!_cases := of_C!_of_C!_of_A!\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 256,
... | [
{
"name": "A!_assoc",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 9,
"n_lines": 24,
"n_chars": 726,
"n_subproofs": 0,
"n_tactics": 31,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 11,
"automation_only": false,
"max_nesting": 8... | 7 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -140,6 +140,9 @@
def of_C_of_C_of_A [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢! φ 🡒 χ) (d₂ : 𝓢 ⊢! ψ 🡒 χ) (d₃ : 𝓢 ⊢! φ ⋎ ψ) : 𝓢 ⊢! χ := or₃ ⨀ d₁ ⨀ d₂ ⨀ d₃
alias A_cases := of_C_of_C_of_A
+lemma of_C!_of_C!_of_A! [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢ φ 🡒 χ) (d₂ : 𝓢 ⊢ ψ 🡒 χ) (d₃ : 𝓢 ⊢ φ ⋎ ψ)... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_10 | 2817c48334a632ed | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 4 | [
{
"theorem_name": "id!",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " nth_axm! 0",
"n_chars": 11,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "nth_axm!",
"text": "lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩\n\n",
"fan_in": 4,
"n_lines": 3,
"n_chars": 103,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0... | [
{
"name": "K!_assoc",
"fan_in": 2,
"n_deps_direct": 6,
"n_deps_transitive": 7,
"n_lines": 16,
"n_chars": 695,
"n_subproofs": 6,
"n_tactics": 27,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max_nesting": 4
... | 2 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -437,6 +437,8 @@
core_finite := by rintro ⟨Γ⟩; simp [AdjunctiveSet.Finite, AdjunctiveSet.set]
def nthAxm {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢]! Γ[n] := conj₂Nth Γ n h
+lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩
+
def byAxm [DecidableEq F] {φ} (h : φ ∈... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_11 | 3493c8497aff8aa7 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 4 | [
{
"theorem_name": "id!",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " nth_axm! 0",
"n_chars": 11,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "nth_axm!",
"text": "lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩\n\n",
"fan_in": 4,
"n_lines": 3,
"n_chars": 103,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0... | [
{
"name": "K!_assoc_mp",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 2,
"n_chars": 111,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1... | 3 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -437,6 +437,8 @@
core_finite := by rintro ⟨Γ⟩; simp [AdjunctiveSet.Finite, AdjunctiveSet.set]
def nthAxm {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢]! Γ[n] := conj₂Nth Γ n h
+lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩
+
def byAxm [DecidableEq F] {φ} (h : φ ∈... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_12 | cce6e4aae7bb9fb2 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 4 | [
{
"theorem_name": "id!",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " nth_axm! 0",
"n_chars": 11,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "nth_axm!",
"text": "lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩\n\n",
"fan_in": 4,
"n_lines": 3,
"n_chars": 103,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0... | [
{
"name": "K!_assoc_mpr",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 3,
"n_chars": 114,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": ... | 3 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -437,6 +437,8 @@
core_finite := by rintro ⟨Γ⟩; simp [AdjunctiveSet.Finite, AdjunctiveSet.set]
def nthAxm {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢]! Γ[n] := conj₂Nth Γ n h
+lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩
+
def byAxm [DecidableEq F] {φ} (h : φ ∈... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_13 | 4e328d1601e1787b | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "cut!",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply deduct'!;\n exact of_C!_of_C!_of_A! (right_A!_intro_left $ of'! (CK!_iff_CC!.mp d₁) ⨀ (K!_left id!)) or₂! (of'! d₂ ⨀ K!_right i... | [
{
"name": "of_C!_of_C!_of_A!",
"text": "lemma of_C!_of_C!_of_A! [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢ φ 🡒 χ) (d₂ : 𝓢 ⊢ ψ 🡒 χ) (d₃ : 𝓢 ⊢ φ ⋎ ψ) : 𝓢 ⊢ χ := ⟨of_C_of_C_of_A d₁.some d₂.some d₃.some⟩\nalias A!_cases := of_C!_of_C!_of_A!\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 256,
... | [
{
"name": "EAAAA!",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 12,
"n_lines": 7,
"n_chars": 170,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": 2
}... | 9 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -140,6 +140,9 @@
def of_C_of_C_of_A [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢! φ 🡒 χ) (d₂ : 𝓢 ⊢! ψ 🡒 χ) (d₃ : 𝓢 ⊢! φ ⋎ ψ) : 𝓢 ⊢! χ := or₃ ⨀ d₁ ⨀ d₂ ⨀ d₃
alias A_cases := of_C_of_C_of_A
+lemma of_C!_of_C!_of_A! [HasAxiomOrElim 𝓢] [ModusPonens 𝓢] (d₁ : 𝓢 ⊢ φ 🡒 χ) (d₂ : 𝓢 ⊢ ψ 🡒 χ) (d₃ : 𝓢 ⊢ φ ⋎ ψ)... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_14 | 616a6dab3663c857 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "EAA!_of_E!_right",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply E!_intro;\n . apply CAA!_of_C!_right; exact K!_left d;\n . apply CAA!_of_C!_right; exact K!_right d;",
"n_char... | [
{
"name": "CAA!_of_C!_right",
"text": "lemma CAA!_of_C!_right (hq : 𝓢 ⊢ ψ 🡒 χ) : 𝓢 ⊢ φ ⋎ ψ 🡒 φ ⋎ χ := ⟨CAA_of_C_right hq.some⟩\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 119,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_st... | [
{
"name": "EAA!_of_E!_right",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 202,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nestin... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -746,6 +746,8 @@
def CAA_of_C_right (hq : 𝓢 ⊢! ψ 🡒 χ) : 𝓢 ⊢! φ ⋎ ψ 🡒 φ ⋎ χ := by
apply deduct';
exact A_replace_right FiniteContext.id (of hq)
+lemma CAA!_of_C!_right (hq : 𝓢 ⊢ ψ 🡒 χ) : 𝓢 ⊢ φ ⋎ ψ 🡒 φ ⋎ χ := ⟨CAA_of_C_right hq.some⟩
+
def A_replace (h : 𝓢 ⊢! φ₁ ⋎ ψ₁) (hp : 𝓢 ⊢! φ₁ 🡒 φ₂) (hq : 𝓢 ⊢!... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_15 | a402d5d14aee24b2 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "EAA!_of_E!_left",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply E!_intro;\n . apply A_replace_left!; exact K!_left d;\n . apply A_replace_left!; exact K!_right d;",
"n_chars":... | [
{
"name": "A_replace_left!",
"text": "lemma A_replace_left! (hp : 𝓢 ⊢ φ 🡒 χ) : 𝓢 ⊢ φ ⋎ ψ 🡒 χ ⋎ ψ := ⟨CAA_of_C_left hp.some⟩\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 117,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_struc... | [
{
"name": "EAA!_of_E!_left",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 199,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nesting... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -742,6 +742,8 @@
def CAA_of_C_left (hp : 𝓢 ⊢! φ 🡒 χ) : 𝓢 ⊢! φ ⋎ ψ 🡒 χ ⋎ ψ := by
apply deduct';
exact A_replace_left FiniteContext.id (of hp)
+lemma A_replace_left! (hp : 𝓢 ⊢ φ 🡒 χ) : 𝓢 ⊢ φ ⋎ ψ 🡒 χ ⋎ ψ := ⟨CAA_of_C_left hp.some⟩
+
def A_replace_right (hc : 𝓢 ⊢! φ ⋎ ψ) (hq : 𝓢 ⊢! ψ 🡒 χ) : 𝓢 ⊢! φ ⋎ ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_16 | 3ddb324d560fa8d1 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "C!_repalce",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n iff_of_E! (ECC!_of_E!_of_E! hp hq)",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "ECC!_of_E!_of_E!",
"text": "lemma ECC!_of_E!_of_E! (hp : 𝓢 ⊢ φ₁ 🡘 φ₂) (hq : 𝓢 ⊢ ψ₁ 🡘 ψ₂) : 𝓢 ⊢ (φ₁ 🡒 ψ₁) 🡘 (φ₂ 🡒 ψ₂) := ⟨ECC_of_E_of_E hp.some hq.some⟩\n\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 184,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_auto... | [
{
"name": "C!_repalce",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 4,
"n_chars": 198,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -762,8 +762,11 @@
apply E_intro;
. apply deduct'; exact C_trans (of $ K_right hp) $ C_trans (FiniteContext.id) (of $ K_left hq);
. apply deduct'; exact C_trans (of $ K_left hp) $ C_trans (FiniteContext.id) (of $ K_right hq);
-lemma C!_repalce [DecidableEq F] (hp : 𝓢 ⊢ φ₁ 🡘 φ₂) (hq : 𝓢 ⊢ ψ₁ 🡘 ψ₂) : 𝓢 ⊢ ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_17 | c5ff00ba96717e3e | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "CConj!_iff_CConj₂",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " C!_iff_C!_of_iff_left $ E!_symm EConj₂Conj!",
"n_chars": 46,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,... | [
{
"name": "C!_iff_C!_of_iff_left",
"text": "lemma C!_iff_C!_of_iff_left (h : 𝓢 ⊢ φ 🡘 ψ) : 𝓢 ⊢ φ 🡒 χ ↔ 𝓢 ⊢ ψ 🡒 χ := by\n constructor;\n . exact C!_trans $ K!_right h;\n . exact C!_trans $ K!_left h;\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 187,
"n_subproofs": 0,
"n_tactics": 7... | [
{
"name": "CConj!_iff_CConj₂",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 3,
"n_chars": 130,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -834,6 +834,11 @@
@[deprecated "use `CCC_of_C_left`"] alias rev_dhyp_imp' := CCC_of_C_left
@[deprecated "use `CCC!_of_C!_left`"] alias rev_dhyp_imp'! := CCC!_of_C!_left
+lemma C!_iff_C!_of_iff_left (h : 𝓢 ⊢ φ 🡘 ψ) : 𝓢 ⊢ φ 🡒 χ ↔ 𝓢 ⊢ ψ 🡒 χ := by
+ constructor;
+ . exact C!_trans $ K!_right h;
+ . exact C!... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_18 | 255a2b540afc10f5 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "right_Fconj!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n right_Conj₂!_intro φ s.toList fun ψ hψ ↦ b ψ (by simpa using hψ)",
"n_chars": 76,
"n_subproofs": 0,
"n_tactics"... | [
{
"name": "right_Conj₂!_intro",
"text": "lemma right_Conj₂!_intro (φ : F) (Γ : List F) (b : (ψ : F) → ψ ∈ Γ → 𝓢 ⊢ φ 🡒 ψ) : 𝓢 ⊢ φ 🡒 ⋀Γ := ⟨right_Conj₂_intro φ Γ (λ ψ hq => (b ψ hq).some)⟩\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 193,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomati... | [
{
"name": "right_Fconj!_intro",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 207,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -325,6 +325,8 @@
| [] => C_of_conseq verum
| [ψ] => by apply b; simp;
| ψ :: χ :: Γ => by apply CK_of_C_of_C (b ψ (by simp)) (right_Conj₂_intro φ _ (fun ψ hq ↦ b ψ (by simp [hq])));
+lemma right_Conj₂!_intro (φ : F) (Γ : List F) (b : (ψ : F) → ψ ∈ Γ → 𝓢 ⊢ φ 🡒 ψ) : 𝓢 ⊢ φ 🡒 ⋀Γ := ⟨right_C... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_19 | 5e4ffbe3b6cad240 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "left_Fconj!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " left_Conj₂!_intro <| by simp [h]",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "left_Conj₂!_intro",
"text": "lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 114,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_st... | [
{
"name": "left_Fconj!_intro",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 3,
"n_chars": 135,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nestin... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -313,6 +313,8 @@
def left_Conj₂_intro [DecidableEq F] {Γ : List F} {φ : F} (h : φ ∈ Γ) : 𝓢 ⊢! ⋀Γ 🡒 φ :=
have : Γ.idxOf φ < Γ.length := List.idxOf_lt_length_of_mem h
cast <| conj₂Nth Γ (Γ.idxOf φ) (by assumption)
+lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩
+
d... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_20 | 93fb790195bce0fc | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "right_Fconj'!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " right_Conj'!_intro φ s.toList ψ (by simpa)",
"n_chars": 45,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1... | [
{
"name": "right_Conj'!_intro",
"text": "lemma right_Conj'!_intro [DecidableEq F] (φ : F) (l : List ι) (ψ : ι → F) (b : ∀ i ∈ l, 𝓢 ⊢ φ 🡒 ψ i) : 𝓢 ⊢ φ 🡒 l.conj' ψ :=\n ⟨right_Conj'_intro φ l ψ fun i hi ↦ (b i hi).get⟩\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 215,
"n_subproofs": 0,
... | [
{
"name": "right_Fconj'!_intro",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 214,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -895,6 +895,9 @@
right_Conj₂_intro φ (l.map ψ) fun χ h ↦
let ⟨i, hi, e⟩ := l.chooseX (fun i ↦ ψ i = χ) (by simpa using h)
e ▸ (b i hi)
+lemma right_Conj'!_intro [DecidableEq F] (φ : F) (l : List ι) (ψ : ι → F) (b : ∀ i ∈ l, 𝓢 ⊢ φ 🡒 ψ i) : 𝓢 ⊢ φ 🡒 l.conj' ψ :=
+ ⟨right_Conj'_intro φ l ψ fun i hi ↦ (... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_21 | a7abbf694b5e33ca | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "left_Fconj'!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n left_Conj'!_intro (by simpa) φ",
"n_chars": 34,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "left_Conj'!_intro",
"text": "lemma left_Conj'!_intro [DecidableEq F] {l : List ι} (h : i ∈ l) (φ : ι → F) : 𝓢 ⊢ l.conj' φ 🡒 φ i := ⟨left_Conj'_intro h φ⟩\n\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automati... | [
{
"name": "left_Fconj'!_intro",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 171,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -896,12 +896,15 @@
let ⟨i, hi, e⟩ := l.chooseX (fun i ↦ ψ i = χ) (by simpa using h)
e ▸ (b i hi)
def left_Conj'_intro [DecidableEq F] {l : List ι} (h : i ∈ l) (φ : ι → F) : 𝓢 ⊢! l.conj' φ 🡒 φ i := left_Conj₂_intro (by simp; use i)
+lemma left_Conj'!_intro [DecidableEq F] {l : List ι} (h : i ∈ l) (φ : ι ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_22 | a1d43052601c68f9 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "right_Fconj'!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " right_Conj'!_intro φ s.toList ψ (by simpa)",
"n_chars": 45,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1... | [
{
"name": "right_Conj'!_intro",
"text": "lemma right_Conj'!_intro [DecidableEq F] (φ : F) (l : List ι) (ψ : ι → F) (b : ∀ i ∈ l, 𝓢 ⊢ φ 🡒 ψ i) : 𝓢 ⊢ φ 🡒 l.conj' ψ :=\n ⟨right_Conj'_intro φ l ψ fun i hi ↦ (b i hi).get⟩\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 215,
"n_subproofs": 0,
... | [
{
"name": "right_Uconj!_intro",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 216,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 2 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -895,6 +895,9 @@
right_Conj₂_intro φ (l.map ψ) fun χ h ↦
let ⟨i, hi, e⟩ := l.chooseX (fun i ↦ ψ i = χ) (by simpa using h)
e ▸ (b i hi)
+lemma right_Conj'!_intro [DecidableEq F] (φ : F) (l : List ι) (ψ : ι → F) (b : ∀ i ∈ l, 𝓢 ⊢ φ 🡒 ψ i) : 𝓢 ⊢ φ 🡒 l.conj' ψ :=
+ ⟨right_Conj'_intro φ l ψ fun i hi ↦ (... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_23 | 155ec784ecf1df21 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "left_Fconj'!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n left_Conj'!_intro (by simpa) φ",
"n_chars": 34,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "left_Conj'!_intro",
"text": "lemma left_Conj'!_intro [DecidableEq F] {l : List ι} (h : i ∈ l) (φ : ι → F) : 𝓢 ⊢ l.conj' φ 🡒 φ i := ⟨left_Conj'_intro h φ⟩\n\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automati... | [
{
"name": "left_Uconj!_intro",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nestin... | 2 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -896,12 +896,15 @@
let ⟨i, hi, e⟩ := l.chooseX (fun i ↦ ψ i = χ) (by simpa using h)
e ▸ (b i hi)
def left_Conj'_intro [DecidableEq F] {l : List ι} (h : i ∈ l) (φ : ι → F) : 𝓢 ⊢! l.conj' φ 🡒 φ i := left_Conj₂_intro (by simp; use i)
+lemma left_Conj'!_intro [DecidableEq F] {l : List ι} (h : i ∈ l) (φ : ι ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_24 | db1db83810b67fc7 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "CConj₂Conj₂!_of_provable",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by induction Γ using List.induction_with_singleton with\n | hnil => exact C!_of_conseq! verum!;\n | hsingle => simp... | [
{
"name": "C!_of_conseq!",
"text": "lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩\nalias dhyp! := C!_of_conseq!\n\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_a... | [
{
"name": "CConj₂Conj₂!_of_provable",
"fan_in": 3,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 359,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"ma... | 2 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -80,6 +80,9 @@
def C_of_conseq [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (h : 𝓢 ⊢! φ) : 𝓢 ⊢! ψ 🡒 φ := implyK ⨀ h
alias dhyp := C_of_conseq
+lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩
+alias dhyp! := C!_of_conseq!
+
class HasAxiomImplyS (𝓢 : S) whe... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_25 | b523fc964e0f30e6 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 25 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "CConj₂Conj₂!_of_provable",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by induction Γ using List.induction_with_singleton with\n | hnil => exact C!_of_conseq! verum!;\n | hsingle => simp... | [
{
"name": "C!_of_conseq!",
"text": "lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩\nalias dhyp! := C!_of_conseq!\n\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_a... | [
{
"name": "CConj₂!_of_forall_provable",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 3,
"n_chars": 170,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"... | 3 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -80,6 +80,9 @@
def C_of_conseq [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (h : 𝓢 ⊢! φ) : 𝓢 ⊢! ψ 🡒 φ := implyK ⨀ h
alias dhyp := C_of_conseq
+lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩
+alias dhyp! := C!_of_conseq!
+
class HasAxiomImplyS (𝓢 : S) whe... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_26 | 9c313849a5b6d168 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 26 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 3 | [
{
"theorem_name": "CConj₂Conj₂!_of_subset",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction Γ using List.induction_with_singleton with\n | hnil => simp;\n | hsingle => simp_all; exact left_Conj₂!_... | [
{
"name": "right_K!_intro",
"text": "lemma right_K!_intro [DecidableEq F] (hq : 𝓢 ⊢ φ 🡒 ψ) (hr : 𝓢 ⊢ φ 🡒 χ) : 𝓢 ⊢ φ 🡒 ψ ⋏ χ := ⟨right_K_intro hq.some hr.some⟩\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation":... | [
{
"name": "CConj₂!_of_unique",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 298,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nest... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -713,6 +713,8 @@
replace hq : [] ⊢[𝓢]! φ 🡒 ψ := of hq;
replace hr : [] ⊢[𝓢]! φ 🡒 χ := of hr;
exact K_intro (mdp' hq FiniteContext.id) (mdp' hr FiniteContext.id)
+lemma right_K!_intro [DecidableEq F] (hq : 𝓢 ⊢ φ 🡒 ψ) (hr : 𝓢 ⊢ φ 🡒 χ) : 𝓢 ⊢ φ 🡒 ψ ⋏ χ := ⟨right_K_intro hq.some hr.some⟩
+
lemma left_... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_27 | 1c151e2797c13844 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 27 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 3 | [
{
"theorem_name": "CConj₂Conj₂!_of_subset",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction Γ using List.induction_with_singleton with\n | hnil => simp;\n | hsingle => simp_all; exact left_Conj₂!_... | [
{
"name": "right_K!_intro",
"text": "lemma right_K!_intro [DecidableEq F] (hq : 𝓢 ⊢ φ 🡒 ψ) (hr : 𝓢 ⊢ φ 🡒 χ) : 𝓢 ⊢ φ 🡒 ψ ⋏ χ := ⟨right_K_intro hq.some hr.some⟩\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation":... | [
{
"name": "C!_of_CConj₂!_of_unique",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 3,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max... | 2 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -713,6 +713,8 @@
replace hq : [] ⊢[𝓢]! φ 🡒 ψ := of hq;
replace hr : [] ⊢[𝓢]! φ 🡒 χ := of hr;
exact K_intro (mdp' hq FiniteContext.id) (mdp' hr FiniteContext.id)
+lemma right_K!_intro [DecidableEq F] (hq : 𝓢 ⊢ φ 🡒 ψ) (hr : 𝓢 ⊢ φ 🡒 χ) : 𝓢 ⊢ φ 🡒 ψ ⋏ χ := ⟨right_K_intro hq.some hr.some⟩
+
lemma left_... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_28 | 37a224a97183ef62 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 28 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "CConj₂Conj₂!_of_provable",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by induction Γ using List.induction_with_singleton with\n | hnil => exact C!_of_conseq! verum!;\n | hsingle => simp... | [
{
"name": "C!_of_conseq!",
"text": "lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩\nalias dhyp! := C!_of_conseq!\n\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_a... | [
{
"name": "CConj₂!_iff_CKConj₂!",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 8,
"n_lines": 11,
"n_chars": 314,
"n_subproofs": 0,
"n_tactics": 16,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max_... | 2 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -80,6 +80,9 @@
def C_of_conseq [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (h : 𝓢 ⊢! φ) : 𝓢 ⊢! ψ 🡒 φ := implyK ⨀ h
alias dhyp := C_of_conseq
+lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩
+alias dhyp! := C!_of_conseq!
+
class HasAxiomImplyS (𝓢 : S) whe... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_29 | 795443102d16e94f | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 29 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 4 | [
{
"theorem_name": "id!",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " nth_axm! 0",
"n_chars": 11,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "nth_axm!",
"text": "lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩\n\n",
"fan_in": 4,
"n_lines": 3,
"n_chars": 103,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0... | [
{
"name": "CKConj₂Remove!_of_CConj₂!",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 4,
"n_chars": 165,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"m... | 3 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -437,6 +437,8 @@
core_finite := by rintro ⟨Γ⟩; simp [AdjunctiveSet.Finite, AdjunctiveSet.set]
def nthAxm {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢]! Γ[n] := conj₂Nth Γ n h
+lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩
+
def byAxm [DecidableEq F] {φ} (h : φ ∈... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_30 | ef20d7b125672992 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 30 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 5 | [
{
"theorem_name": "CConj₂AppendKConj₂Conj₂!",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply FiniteContext.deduct'!;\n have : [⋀(Γ ++ Δ)] ⊢[𝓢] ⋀(Γ ++ Δ) := id!;\n have d := Conj₂!_iff_forall_provab... | [
{
"name": "Conj₂!_iff_forall_provable",
"text": "lemma Conj₂!_iff_forall_provable [DecidableEq F] {Γ : List F} : (𝓢 ⊢ ⋀Γ) ↔ (∀ φ ∈ Γ, 𝓢 ⊢ φ) := by\n induction Γ using List.induction_with_singleton with\n | hnil => simp;\n | hsingle => simp;\n | hcons φ Γ hΓ ih =>\n simp_all;\n constructor;\n ... | [
{
"name": "Conj₂Append!_iff_KConj₂Conj₂!",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 18,
"n_chars": 725,
"n_subproofs": 0,
"n_tactics": 35,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 14,
"automation_only": false,... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -901,6 +901,20 @@
lemma left_Fconj!_intro [DecidableEq F] {s : Finset F} (h : φ ∈ s) : 𝓢 ⊢ s.conj 🡒 φ := left_Conj₂!_intro <| by simp [h]
+lemma Conj₂!_iff_forall_provable [DecidableEq F] {Γ : List F} : (𝓢 ⊢ ⋀Γ) ↔ (∀ φ ∈ Γ, 𝓢 ⊢ φ) := by
+ induction Γ using List.induction_with_singleton with
+ | hnil => si... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_31 | 5b1db53ad3abf422 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 31 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 4 | [
{
"theorem_name": "id!",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " nth_axm! 0",
"n_chars": 11,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "nth_axm!",
"text": "lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩\n\n",
"fan_in": 4,
"n_lines": 3,
"n_chars": 103,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0... | [
{
"name": "CConj₂Append!_iff_CKConj₂Conj₂!",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 11,
"n_lines": 6,
"n_chars": 299,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,... | 4 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -437,6 +437,8 @@
core_finite := by rintro ⟨Γ⟩; simp [AdjunctiveSet.Finite, AdjunctiveSet.set]
def nthAxm {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢]! Γ[n] := conj₂Nth Γ n h
+lemma nth_axm! {Γ} (n : ℕ) (h : n < Γ.length := by simp) : Γ ⊢[𝓢] Γ[n] := ⟨nthAxm n h⟩
+
def byAxm [DecidableEq F] {φ} (h : φ ∈... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_32 | 06beb0ac36bb96e6 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 32 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "left_Fconj!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " left_Conj₂!_intro <| by simp [h]",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "left_Conj₂!_intro",
"text": "lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 114,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_st... | [
{
"name": "FConj_DT'",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 30,
"n_lines": 6,
"n_chars": 331,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nesting": 2
... | 17 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -313,6 +313,8 @@
def left_Conj₂_intro [DecidableEq F] {Γ : List F} {φ : F} (h : φ ∈ Γ) : 𝓢 ⊢! ⋀Γ 🡒 φ :=
have : Γ.idxOf φ < Γ.length := List.idxOf_lt_length_of_mem h
cast <| conj₂Nth Γ (Γ.idxOf φ) (by assumption)
+lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩
+
d... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_33 | e2e36a592066b85c | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 33 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "CConj₂Conj₂!_of_provable",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by induction Γ using List.induction_with_singleton with\n | hnil => exact C!_of_conseq! verum!;\n | hsingle => simp... | [
{
"name": "C!_of_conseq!",
"text": "lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩\nalias dhyp! := C!_of_conseq!\n\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_a... | [
{
"name": "CFconjFconj!_of_provable",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 11,
"n_chars": 419,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"... | 5 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -80,6 +80,9 @@
def C_of_conseq [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (h : 𝓢 ⊢! φ) : 𝓢 ⊢! ψ 🡒 φ := implyK ⨀ h
alias dhyp := C_of_conseq
+lemma C!_of_conseq! [ModusPonens 𝓢] [HasAxiomImplyK 𝓢] (d : 𝓢 ⊢ φ) : 𝓢 ⊢ ψ 🡒 φ := ⟨C_of_conseq d.some⟩
+alias dhyp! := C!_of_conseq!
+
class HasAxiomImplyS (𝓢 : S) whe... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_34 | 375daa3e854d9bfd | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 34 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "right_Fdisj'!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n right_Disj'!_intro _ _ (by simp [hi])",
"n_chars": 40,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "right_Disj'!_intro",
"text": "lemma right_Disj'!_intro [DecidableEq F] (φ : ι → F) (l : List ι) (h : i ∈ l) : 𝓢 ⊢ φ i 🡒 l.disj' φ := ⟨right_Disj'_intro φ l h⟩\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 152,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "right_Fdisj'!_intro",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 176,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -1075,8 +1075,11 @@
def right_Disj'_intro [DecidableEq F] (φ : ι → F) (l : List ι) (h : i ∈ l) : 𝓢 ⊢! φ i 🡒 l.disj' φ :=
right_Disj₂_intro (l.map φ) (by simpa using ⟨i, h, rfl⟩)
-lemma right_Fdisj'!_intro [DecidableEq F] (s : Finset ι) (φ : ι → F) {i} (hi : i ∈ s) : 𝓢 ⊢ φ i 🡒 ⩖ j ∈ s, φ j := sorry
+lemma r... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_35 | ec035f5bcc08273e | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 35 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 1 | [
{
"theorem_name": "right_Fdisj'!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n right_Disj'!_intro _ _ (by simp [hi])",
"n_chars": 40,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "right_Disj'!_intro",
"text": "lemma right_Disj'!_intro [DecidableEq F] (φ : ι → F) (l : List ι) (h : i ∈ l) : 𝓢 ⊢ φ i 🡒 l.disj' φ := ⟨right_Disj'_intro φ l h⟩\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 152,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "right_Udisj!_intro",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 3,
"n_chars": 141,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 2 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -1075,8 +1075,11 @@
def right_Disj'_intro [DecidableEq F] (φ : ι → F) (l : List ι) (h : i ∈ l) : 𝓢 ⊢! φ i 🡒 l.disj' φ :=
right_Disj₂_intro (l.map φ) (by simpa using ⟨i, h, rfl⟩)
-lemma right_Fdisj'!_intro [DecidableEq F] (s : Finset ι) (φ : ι → F) {i} (hi : i ∈ s) : 𝓢 ⊢ φ i 🡒 ⩖ j ∈ s, φ j := sorry
+lemma r... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_36 | 10e21b1bd454aae4 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 36 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "left_Fconj!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " left_Conj₂!_intro <| by simp [h]",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "left_Conj₂!_intro",
"text": "lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 114,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_st... | [
{
"name": "CFConj_CDisj!_of_K_intro",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 15,
"n_lines": 13,
"n_chars": 580,
"n_subproofs": 0,
"n_tactics": 22,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": false,
... | 9 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -313,6 +313,8 @@
def left_Conj₂_intro [DecidableEq F] {Γ : List F} {φ : F} (h : φ ∈ Γ) : 𝓢 ⊢! ⋀Γ 🡒 φ :=
have : Γ.idxOf φ < Γ.length := List.idxOf_lt_length_of_mem h
cast <| conj₂Nth Γ (Γ.idxOf φ) (by assumption)
+lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩
+
d... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_37 | 8c9174efa861aef9 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 37 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "left_Fconj!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " left_Conj₂!_intro <| by simp [h]",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "left_Conj₂!_intro",
"text": "lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 114,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_st... | [
{
"name": "CFConj_CDisj!_of_innerMDP",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 15,
"n_lines": 14,
"n_chars": 646,
"n_subproofs": 2,
"n_tactics": 23,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
... | 9 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -313,6 +313,8 @@
def left_Conj₂_intro [DecidableEq F] {Γ : List F} {φ : F} (h : φ ∈ Γ) : 𝓢 ⊢! ⋀Γ 🡒 φ :=
have : Γ.idxOf φ < Γ.length := List.idxOf_lt_length_of_mem h
cast <| conj₂Nth Γ (Γ.idxOf φ) (by assumption)
+lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩
+
d... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_38 | 8d0bf19617abae5d | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 38 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "left_Fconj!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " left_Conj₂!_intro <| by simp [h]",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "left_Conj₂!_intro",
"text": "lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 114,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_st... | [
{
"name": "iff_FiniteContext_Context",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 12,
"n_chars": 373,
"n_subproofs": 0,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
... | 4 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -313,6 +313,8 @@
def left_Conj₂_intro [DecidableEq F] {Γ : List F} {φ : F} (h : φ ∈ Γ) : 𝓢 ⊢! ⋀Γ 🡒 φ :=
have : Γ.idxOf φ < Γ.length := List.idxOf_lt_length_of_mem h
cast <| conj₂Nth Γ (Γ.idxOf φ) (by assumption)
+lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩
+
d... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_39 | 9604655f99fe6e1b | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 39 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 5 | [
{
"theorem_name": "CConj₂AppendKConj₂Conj₂!",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply FiniteContext.deduct'!;\n have : [⋀(Γ ++ Δ)] ⊢[𝓢] ⋀(Γ ++ Δ) := id!;\n have d := Conj₂!_iff_forall_provab... | [
{
"name": "Conj₂!_iff_forall_provable",
"text": "lemma Conj₂!_iff_forall_provable [DecidableEq F] {Γ : List F} : (𝓢 ⊢ ⋀Γ) ↔ (∀ φ ∈ Γ, 𝓢 ⊢ φ) := by\n induction Γ using List.induction_with_singleton with\n | hnil => simp;\n | hsingle => simp;\n | hcons φ Γ hΓ ih =>\n simp_all;\n constructor;\n ... | [
{
"name": "FConj'_iff_forall_provable",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 356,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"... | 1 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -901,6 +901,20 @@
lemma left_Fconj!_intro [DecidableEq F] {s : Finset F} (h : φ ∈ s) : 𝓢 ⊢ s.conj 🡒 φ := left_Conj₂!_intro <| by simp [h]
+lemma Conj₂!_iff_forall_provable [DecidableEq F] {Γ : List F} : (𝓢 ⊢ ⋀Γ) ↔ (∀ φ ∈ Γ, 𝓢 ⊢ φ) := by
+ induction Γ using List.induction_with_singleton with
+ | hnil => si... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_b114d31242b6_40 | 5f690fc7ed9260ee | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Entailment/Minimal/Basic.lean | Basic | 40 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 43 | 2 | [
{
"theorem_name": "left_Fconj!_intro",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " left_Conj₂!_intro <| by simp [h]",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "left_Conj₂!_intro",
"text": "lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 114,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_st... | [
{
"name": "provable_iff_finset",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 19,
"n_chars": 557,
"n_subproofs": 0,
"n_tactics": 33,
"cyclomatic": 8,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 13,
"automation_only": false,
"max_... | 4 | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | module
public import Foundation.Logic.Entailment
public import Foundation.Vorspiel.Finset.Basic
@[expose] public section
namespace LO.Axioms
variable {F : Type*} [LogicalConnective F]
variable (φ ψ χ : F)
protected abbrev NegEquiv := ∼φ 🡘 (φ 🡒 ⊥)
protected abbrev Verum : F := ⊤
protected abbrev ImplyK := φ 🡒 ... | @@ -313,6 +313,8 @@
def left_Conj₂_intro [DecidableEq F] {Γ : List F} {φ : F} (h : φ ∈ Γ) : 𝓢 ⊢! ⋀Γ 🡒 φ :=
have : Γ.idxOf φ < Γ.length := List.idxOf_lt_length_of_mem h
cast <| conj₂Nth Γ (Γ.idxOf φ) (by assumption)
+lemma left_Conj₂!_intro [DecidableEq F] (h : φ ∈ Γ) : 𝓢 ⊢ ⋀Γ 🡒 φ := ⟨left_Conj₂_intro h⟩
+
d... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_0 | 608a2ea86daa9655 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "val_rew",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction t <;> simp [*, -val_func, val_func']",
"n_chars": 52,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
... | [
{
"name": "val_func'",
"text": "lemma val_func' {k} (F : L.Func k) (v) :\n (func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 116,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites... | [
{
"name": "val_rew",
"fan_in": 12,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -97,8 +97,12 @@
@[simp] lemma val_func {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F (Semiterm.val b f ∘ v) := rfl
+lemma val_func' {k} (F : L.Func k) (v) :
+ (func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+
lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
- ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_1 | 93df8103bbb7a3ec | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_rewrite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 173,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,17 +100,24 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_2 | 2a0e17571cab636b | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_rewriteMap",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,17 +100,24 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_3 | de83968bc16158a6 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_substs",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 173,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,17 +100,24 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_4 | b1a8f4bf43b9ffd0 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_bShift",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 144,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 1
... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_5 | f9548a0a8bed2c3f | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_bShift'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 156,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 1
... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,17 +100,23 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_6 | 7881b1c355de274b | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_embSubsts",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 182,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,17 +100,24 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_7 | 442c55771896cd6d | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_shift",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 128,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1
... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_8 | 94469b489fc138ad | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_free",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 201,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2
... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_9 | 8f3dce479404dcca | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "val_fix",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 247,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
}... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_10 | 533d8c9848e27e19 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "ofEquiv_val",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction t <;> simp [*, Semiterm.val_func, ofEquiv_func Θ, Function.comp_def]",
"n_chars": 85,
"n_subproofs": 0,
"... | [
{
"name": "ofEquiv_func",
"text": "lemma ofEquiv_func (f : L.Func k) (v : Fin k → N) :\n (ofEquiv Θ).func f v = Θ (func f (Θ.symm ∘ v)) := rfl\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 118,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites... | [
{
"name": "ofEquiv_val",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 241,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2... | 1 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -156,8 +156,12 @@
variable [s : Structure L M] (Θ : M ≃ N)
+lemma ofEquiv_func (f : L.Func k) (v : Fin k → N) :
+ (ofEquiv Θ).func f v = Θ (func f (Θ.symm ∘ v)) := rfl
+
lemma ofEquiv_val (b : Fin n → N) (f : ξ → N) (t : Semiterm L ξ n) :
- t.val (s := ofEquiv Θ) b f = Θ (t.val (Θ.symm ∘ b) (Θ.symm ∘ f))... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_11 | 89664bf2d41d5dcf | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "eval_rew_q",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 11,
"n_chars": 467,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting": 4... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_12 | be126e2fefa4e8c7 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "eval_map",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 5,
"n_chars": 265,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_13 | 26be917bccff0f9a | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "eval_rewrite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 5,
"n_chars": 211,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_14 | 080564820980a52f | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "eval_rewriteMap",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 5,
"n_chars": 216,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_15 | 47e079aab1c9889d | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 12 | [
{
"theorem_name": "val_rewrite",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [val_rew]; congr",
"n_chars": 27,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1... | [
{
"name": "val_rew",
"text": "lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :\n (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by\n induction t <;> simp [*, -val_func, val_func']\n\n",
"fan_in": 12,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
... | [
{
"name": "eval_bShift'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -100,14 +100,20 @@
lemma val_func' {k} (F : L.Func k) (v) :
(func F v).val b f = s.func F fun i ↦ Semiterm.val b f (v i) := rfl
+lemma val_rew (ω : Rew L ξ₁ n₁ ξ₂ n₂) (t : Semiterm L ξ₁ n₁) :
+ (ω t).val b₂ f₂ = t.val (val b₂ f₂ ∘ ω ∘ bvar) (val b₂ f₂ ∘ ω ∘ fvar) := by
+ induction t <;> simp [*, -val_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_16 | 00a8e3bf731a2593 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "eval_iff_of_funEqOn",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n match φ with\n | .rel r v =>\n simp only [eval_rel]; apply iff_of_eq; congr 1\n funext i\n exact Semiterm.v... | [
{
"name": "val_eq_of_funEqOn",
"text": "lemma val_eq_of_funEqOn [DecidableEq ξ] (t : Semiterm L ξ n) (h : Function.funEqOn t.FVar? f f') :\n t.val b f = t.val b f' := by\n induction t\n case bvar => simp\n case fvar x =>\n exact h x (by simp [FVar?])\n case func k f v ih =>\n simp only [val_fun... | [
{
"name": "eval_iff_of_funEqOn",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 32,
"n_chars": 1470,
"n_subproofs": 4,
"n_tactics": 35,
"cyclomatic": 2,
"n_automation": 13,
"n_rewrites": 2,
"n_structural": 18,
"automation_only": false,
"ma... | 1 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -127,6 +127,16 @@
end Syntactic
+lemma val_eq_of_funEqOn [DecidableEq ξ] (t : Semiterm L ξ n) (h : Function.funEqOn t.FVar? f f') :
+ t.val b f = t.val b f' := by
+ induction t
+ case bvar => simp
+ case fvar x =>
+ exact h x (by simp [FVar?])
+ case func k f v ih =>
+ simp only [val_func, Function... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_17 | 5f5c40cfdb0f7722 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "eval_toEmpty",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n match φ with\n | .rel r v =>\n simp only [eval_rel]\n apply iff_of_eq; congr 2; funext i\n simpa [Semiterm.val_toE... | [
{
"name": "val_toEmpty",
"text": "lemma val_toEmpty [DecidableEq ξ] (t : Semiterm L ξ n) (h : t.freeVariables = ∅) : t.val b f = (t.toEmpty h).valb b := by\n induction t\n case bvar => simp [Semiterm.toEmpty]\n case fvar => simp at h\n case func k f v ih =>\n simp only [val_func]\n have : ∀ i, (v ... | [
{
"name": "eval_toEmpty",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 23,
"n_chars": 988,
"n_subproofs": 2,
"n_tactics": 25,
"cyclomatic": 2,
"n_automation": 12,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": false,
"max_nesting... | 1 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -137,6 +137,17 @@
simp only [val_func, Function.comp_def]
congr; funext i; exact ih i (by intro x hx; exact h x (by simpa using ⟨i, hx⟩))
+lemma val_toEmpty [DecidableEq ξ] (t : Semiterm L ξ n) (h : t.freeVariables = ∅) : t.val b f = (t.toEmpty h).valb b := by
+ induction t
+ case bvar => simp [Semiter... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_18 | c5c05f01da9219f8 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 2 | [
{
"theorem_name": "eval_univCl'",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [univCl', eval_allClosure, eval_rew, Matrix.empty_eq, Function.comp_def]\n constructor\n · intro h g\n refine (... | [
{
"name": "eval_iff_of_funEqOn",
"text": "lemma eval_iff_of_funEqOn [DecidableEq ξ] {n b} (φ : Semiformula L ξ n) (h : Function.funEqOn φ.FVar? f f') :\n Eval b f φ ↔ Eval b f' φ := by\n match φ with\n | .rel r v =>\n simp only [eval_rel]; apply iff_of_eq; congr 1\n funext i\n exact Semiterm.... | [
{
"name": "eval_enumarateFVar_idxOfFVar_eq_id",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 336,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": fals... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -308,6 +308,37 @@
end Syntactic
+lemma eval_iff_of_funEqOn [DecidableEq ξ] {n b} (φ : Semiformula L ξ n) (h : Function.funEqOn φ.FVar? f f') :
+ Eval b f φ ↔ Eval b f' φ := by
+ match φ with
+ | .rel r v =>
+ simp only [eval_rel]; apply iff_of_eq; congr 1
+ funext i
+ exact Semiterm.val_eq_of_fun... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_19 | 3363686cfb16aa0e | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "eval_ofEquiv_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n match φ with\n | .rel r v | .nrel r v => by simp [Function.comp_def, ofEquiv_rel Θ, Structure.ofEquiv_val Θ]\n | ⊤ | ⊥ => ... | [
{
"name": "ofEquiv_val",
"text": "lemma ofEquiv_val (b : Fin n → N) (f : ξ → N) (t : Semiterm L ξ n) :\n t.val (s := ofEquiv Θ) b f = Θ (t.val (Θ.symm ∘ b) (Θ.symm ∘ f)) := by\n induction t <;> simp [*, Semiterm.val_func, ofEquiv_func Θ, Function.comp_def]\n\n",
"fan_in": 1,
"n_lines": 5,
"n... | [
{
"name": "eval_ofEquiv_iff",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 14,
"n_chars": 912,
"n_subproofs": 2,
"n_tactics": 21,
"cyclomatic": 4,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": false,
"max_nest... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -159,6 +159,10 @@
lemma ofEquiv_func (f : L.Func k) (v : Fin k → N) :
(ofEquiv Θ).func f v = Θ (func f (Θ.symm ∘ v)) := rfl
+lemma ofEquiv_val (b : Fin n → N) (f : ξ → N) (t : Semiterm L ξ n) :
+ t.val (s := ofEquiv Θ) b f = Θ (t.val (Θ.symm ∘ b) (Θ.symm ∘ f)) := by
+ induction t <;> simp [*, Semiterm.va... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_20 | 2176a9efaaae30df | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "eval_ofEquiv_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n match φ with\n | .rel r v | .nrel r v => by simp [Function.comp_def, ofEquiv_rel Θ, Structure.ofEquiv_val Θ]\n | ⊤ | ⊥ => ... | [
{
"name": "ofEquiv_val",
"text": "lemma ofEquiv_val (b : Fin n → N) (f : ξ → N) (t : Semiterm L ξ n) :\n t.val (s := ofEquiv Θ) b f = Θ (t.val (Θ.symm ∘ b) (Θ.symm ∘ f)) := by\n induction t <;> simp [*, Semiterm.val_func, ofEquiv_func Θ, Function.comp_def]\n\n",
"fan_in": 1,
"n_lines": 5,
"n... | [
{
"name": "evalf_ofEquiv_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 4,
"n_chars": 210,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nestin... | 4 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -159,6 +159,10 @@
lemma ofEquiv_func (f : L.Func k) (v : Fin k → N) :
(ofEquiv Θ).func f v = Θ (func f (Θ.symm ∘ v)) := rfl
+lemma ofEquiv_val (b : Fin n → N) (f : ξ → N) (t : Semiterm L ξ n) :
+ t.val (s := ofEquiv Θ) b f = Θ (t.val (Θ.symm ∘ b) (Θ.symm ∘ f)) := by
+ induction t <;> simp [*, Semiterm.va... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_21 | 8160912fba738cef | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 2 | [
{
"theorem_name": "models_iff_proposition",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [models_iff]",
"n_chars": 23,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automat... | [
{
"name": "models_iff",
"text": "lemma models_iff : M↓[L] ⊧ σ ↔ σ.Realize M := by rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | [
{
"name": "models_iff_proposition",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 135,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_n... | 1 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -426,8 +426,11 @@
variable {M}
-lemma models_iff_proposition {φ : Proposition L} : M↓[L] ⊧ φ.univCl ↔ ∀ f : ℕ → M, φ.Evalf f := sorry
+lemma models_iff : M↓[L] ⊧ σ ↔ σ.Realize M := by rfl
+lemma models_iff_proposition {φ : Proposition L} : M↓[L] ⊧ φ.univCl ↔ ∀ f : ℕ → M, φ.Evalf f := by
+ simp [models_iff]
+... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_22 | cc7d77cbd54a1473 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 2 | [
{
"theorem_name": "models_iff_proposition",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [models_iff]",
"n_chars": 23,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automat... | [
{
"name": "models_iff",
"text": "lemma models_iff : M↓[L] ⊧ σ ↔ σ.Realize M := by rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | [
{
"name": "consequence_iff_unsatisfiable",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 15,
"n_chars": 636,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": false,
... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -426,6 +426,8 @@
variable {M}
+lemma models_iff : M↓[L] ⊧ σ ↔ σ.Realize M := by rfl
+
variable (M T)
variable {M T}
@@ -460,8 +462,16 @@
lemma consequence_iff_unsatisfiable {σ : Sentence L} :
T ⊨[Struc.{v, u} L] σ ↔ ¬Semantics.Satisfiable (Struc.{v, u} L) (insert (∼σ) T) := by
constructor
- · sorr... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_23 | dbec0bd8fb58634e | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "eval_lMap",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction φ using rec' <;>\n simp [*, Semiterm.val_lMap, lMap_rel, lMap_nrel, eval_rel, eval_nrel, Function.comp_def]",
"n... | [
{
"name": "val_lMap",
"text": "lemma val_lMap (φ : L₁ →ᵥ L₂) (s₂ : Structure L₂ M) (b : Fin n → M) (f : ξ → M) {t : Semiterm L₁ ξ n} :\n (t.lMap φ).val (s := s₂) b f = t.val (s := s₂.lMap φ) b f := by\n induction t <;> simp [*, val_func, Semiterm.lMap_func, Function.comp_def]\n\n",
"fan_in": 1,
... | [
{
"name": "eval_lMap",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 6,
"n_chars": 264,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 4
... | 1 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -119,6 +119,10 @@
variable (φ : L₁ →ᵥ L₂) (b : Fin n → M) (f : ξ → M)
+lemma val_lMap (φ : L₁ →ᵥ L₂) (s₂ : Structure L₂ M) (b : Fin n → M) (f : ξ → M) {t : Semiterm L₁ ξ n} :
+ (t.lMap φ).val (s := s₂) b f = t.val (s := s₂.lMap φ) b f := by
+ induction t <;> simp [*, val_func, Semiterm.lMap_func, Function.c... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_24 | 5c4fb7efbf9efe34 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "eval_lMap",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction φ using rec' <;>\n simp [*, Semiterm.val_lMap, lMap_rel, lMap_nrel, eval_rel, eval_nrel, Function.comp_def]",
"n... | [
{
"name": "val_lMap",
"text": "lemma val_lMap (φ : L₁ →ᵥ L₂) (s₂ : Structure L₂ M) (b : Fin n → M) (f : ξ → M) {t : Semiterm L₁ ξ n} :\n (t.lMap φ).val (s := s₂) b f = t.val (s := s₂.lMap φ) b f := by\n induction t <;> simp [*, val_func, Semiterm.lMap_func, Function.comp_def]\n\n",
"fan_in": 1,
... | [
{
"name": "models_lMap",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 5,
"n_chars": 164,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
... | 2 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -119,6 +119,10 @@
variable (φ : L₁ →ᵥ L₂) (b : Fin n → M) (f : ξ → M)
+lemma val_lMap (φ : L₁ →ᵥ L₂) (s₂ : Structure L₂ M) (b : Fin n → M) (f : ξ → M) {t : Semiterm L₁ ξ n} :
+ (t.lMap φ).val (s := s₂) b f = t.val (s := s₂.lMap φ) b f := by
+ induction t <;> simp [*, val_func, Semiterm.lMap_func, Function.c... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ba9acceb3a2e_25 | 9832161079208ccf | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Semantics/Semantics.lean | Semantics | 25 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "models_lMap",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Semantics.Models, eval_lMap]",
"n_chars": 40,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_a... | [
{
"name": "eval_lMap",
"text": "lemma eval_lMap [Nonempty M] {φ : Semiformula L₁ ξ n} :\n Eval (s := s₂) b f (lMap Φ φ) ↔ Eval (s := s₂.lMap Φ) b f φ := by\n induction φ using rec' <;>\n simp [*, Semiterm.val_lMap, lMap_rel, lMap_nrel, eval_rel, eval_nrel, Function.comp_def]\n\n",
"fan_in": 1,
... | [
{
"name": "lMap_models_lMap",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 9,
"n_chars": 414,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 3 | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | module
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Foundation.Vorspiel.IsEmpty
public import Foundation.Vorspiel.Empty
@[expose] public section
/-!
# Model-theoretic semantics of first-order classical logic
This file defines the structure and the evaluation of terms and formulas by Tarski's t... | @@ -466,8 +466,14 @@
section lMap
variable {M : Type u} {s₂ : Structure L₂ M} {n} {b : Fin n → M} {f : ξ → M}
+lemma eval_lMap [Nonempty M] {φ : Semiformula L₁ ξ n} :
+ Eval (s := s₂) b f (lMap Φ φ) ↔ Eval (s := s₂.lMap Φ) b f φ := by
+ induction φ using rec' <;>
+ simp [*, Semiterm.val_lMap, lMap_rel, lMap_... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_8ab3cf5fb67e_0 | 01dbe41371aea015 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Modal/Kripke/ComplexityLimited.lean | ComplexityLimited | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "iff_satisfy_complexityLimitedModel",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply iff_satisfy_complexityLimitedModel_aux (show φ ∈ φ.subformulas by simp);\n use 0; simp;",
"n_... | [
{
"name": "iff_satisfy_complexityLimitedModel_aux",
"text": "lemma iff_satisfy_complexityLimitedModel_aux\n (hq : ψ ∈ φ.subformulas)\n (hx : ∃ n ≤ φ.complexity - ψ.complexity, r ≺^[n] x)\n :\n haveI : x ∈ {y | ∃ n ≤ φ.complexity, r ≺^[n] y} := by obtain ⟨n, _, _⟩ := hx; use n; exact ⟨by omega, by assump... | [
{
"name": "iff_satisfy_complexityLimitedModel",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 234,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": fals... | 1 | module
public import Foundation.Modal.Kripke.Basic
@[expose] public section
namespace LO.Modal.Kripke
def complexityLimitedFrame (F : Kripke.Frame) (r : F.World) (φ : Formula ℕ) : Kripke.Frame where
World := { x | ∃ n ≤ φ.complexity, r ≺^[n] x }
Rel x y := x.1 ≺ y.1
world_nonempty := ⟨r, by use 0; simp⟩
def ... | module
public import Foundation.Modal.Kripke.Basic
@[expose] public section
namespace LO.Modal.Kripke
def complexityLimitedFrame (F : Kripke.Frame) (r : F.World) (φ : Formula ℕ) : Kripke.Frame where
World := { x | ∃ n ≤ φ.complexity, r ≺^[n] x }
Rel x y := x.1 ≺ y.1
world_nonempty := ⟨r, by use 0; simp⟩
def ... | @@ -22,8 +22,58 @@
open Formula.Kripke
open Formula
-lemma iff_satisfy_complexityLimitedModel : r ⊧ φ ↔ Satisfies (complexityLimitedModel M r φ) ⟨r, (by use 0; simp)⟩ φ := sorry
+lemma iff_satisfy_complexityLimitedModel_aux
+ (hq : ψ ∈ φ.subformulas)
+ (hx : ∃ n ≤ φ.complexity - ψ.complexity, r ≺^[n] x)
+ :
+ h... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_8ab3cf5fb67e_1 | 1dfc8fa572c9cfce | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Modal/Kripke/ComplexityLimited.lean | ComplexityLimited | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "iff_satisfy_complexityLimitedModel",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply iff_satisfy_complexityLimitedModel_aux (show φ ∈ φ.subformulas by simp);\n use 0; simp;",
"n_... | [
{
"name": "iff_satisfy_complexityLimitedModel_aux",
"text": "lemma iff_satisfy_complexityLimitedModel_aux\n (hq : ψ ∈ φ.subformulas)\n (hx : ∃ n ≤ φ.complexity - ψ.complexity, r ≺^[n] x)\n :\n haveI : x ∈ {y | ∃ n ≤ φ.complexity, r ≺^[n] y} := by obtain ⟨n, _, _⟩ := hx; use n; exact ⟨by omega, by assump... | [
{
"name": "complexityLimitedModel_subformula_closedAux",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 517,
"n_subproofs": 0,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 5,
"automation_o... | 1 | module
public import Foundation.Modal.Kripke.Basic
@[expose] public section
namespace LO.Modal.Kripke
def complexityLimitedFrame (F : Kripke.Frame) (r : F.World) (φ : Formula ℕ) : Kripke.Frame where
World := { x | ∃ n ≤ φ.complexity, r ≺^[n] x }
Rel x y := x.1 ≺ y.1
world_nonempty := ⟨r, by use 0; simp⟩
def ... | module
public import Foundation.Modal.Kripke.Basic
@[expose] public section
namespace LO.Modal.Kripke
def complexityLimitedFrame (F : Kripke.Frame) (r : F.World) (φ : Formula ℕ) : Kripke.Frame where
World := { x | ∃ n ≤ φ.complexity, r ≺^[n] x }
Rel x y := x.1 ≺ y.1
world_nonempty := ⟨r, by use 0; simp⟩
def ... | @@ -22,8 +22,61 @@
open Formula.Kripke
open Formula
+lemma iff_satisfy_complexityLimitedModel_aux
+ (hq : ψ ∈ φ.subformulas)
+ (hx : ∃ n ≤ φ.complexity - ψ.complexity, r ≺^[n] x)
+ :
+ haveI : x ∈ {y | ∃ n ≤ φ.complexity, r ≺^[n] y} := by obtain ⟨n, _, _⟩ := hx; use n; exact ⟨by omega, by assumption⟩;
+ x ⊧ ψ ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_8ab3cf5fb67e_2 | 5a0e781295e9f310 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Modal/Kripke/ComplexityLimited.lean | ComplexityLimited | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "iff_satisfy_complexityLimitedModel",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply iff_satisfy_complexityLimitedModel_aux (show φ ∈ φ.subformulas by simp);\n use 0; simp;",
"n_... | [
{
"name": "iff_satisfy_complexityLimitedModel_aux",
"text": "lemma iff_satisfy_complexityLimitedModel_aux\n (hq : ψ ∈ φ.subformulas)\n (hx : ∃ n ≤ φ.complexity - ψ.complexity, r ≺^[n] x)\n :\n haveI : x ∈ {y | ∃ n ≤ φ.complexity, r ≺^[n] y} := by obtain ⟨n, _, _⟩ := hx; use n; exact ⟨by omega, by assump... | [
{
"name": "complexityLimitedModel_subformula_closed",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 384,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automation_only"... | 2 | module
public import Foundation.Modal.Kripke.Basic
@[expose] public section
namespace LO.Modal.Kripke
def complexityLimitedFrame (F : Kripke.Frame) (r : F.World) (φ : Formula ℕ) : Kripke.Frame where
World := { x | ∃ n ≤ φ.complexity, r ≺^[n] x }
Rel x y := x.1 ≺ y.1
world_nonempty := ⟨r, by use 0; simp⟩
def ... | module
public import Foundation.Modal.Kripke.Basic
@[expose] public section
namespace LO.Modal.Kripke
def complexityLimitedFrame (F : Kripke.Frame) (r : F.World) (φ : Formula ℕ) : Kripke.Frame where
World := { x | ∃ n ≤ φ.complexity, r ≺^[n] x }
Rel x y := x.1 ≺ y.1
world_nonempty := ⟨r, by use 0; simp⟩
def ... | @@ -22,8 +22,61 @@
open Formula.Kripke
open Formula
+lemma iff_satisfy_complexityLimitedModel_aux
+ (hq : ψ ∈ φ.subformulas)
+ (hx : ∃ n ≤ φ.complexity - ψ.complexity, r ≺^[n] x)
+ :
+ haveI : x ∈ {y | ∃ n ≤ φ.complexity, r ≺^[n] y} := by obtain ⟨n, _, _⟩ := hx; use n; exact ⟨by omega, by assumption⟩;
+ x ⊧ ψ ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_db6a2c2b28b6_0 | 02bc1bec50f4806b | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Arithmetic/Definability/BoundedDefinable.lean | BoundedDefinable | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 6 | [
{
"theorem_name": "ball_blt",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hf.bounded with ⟨bf, hbf⟩\n have : ℌ.Definable fun v ↦ ∃ x ≤ bf.val v id, x = f v ∧ ∀ y < x, P v y := by\n apply bexs';... | [
{
"name": "of_iff",
"text": "lemma of_iff {f g : (Fin k → V) → V} (H : DefinableBoundedFunction f) (h : ∀ v, f v = g v) : DefinableBoundedFunction g := by\n have : f = g := by funext v; simp [h]\n rcases this; exact H\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 196,
"n_subproofs": 1,
"... | [
{
"name": "ball_blt",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 711,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": false,
"max_nesting": 6
... | 1 | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | @@ -140,19 +140,51 @@
lemma ball_blt {P : (Fin k → V) → V → Prop} {f : (Fin k → V) → V}
(hf : DefinableBoundedFunction f) (h : ℌ.Definable fun w ↦ P (w ·.succ) (w 0)) :
- ℌ.Definable fun v ↦ ∀ x < f v, P v x := sorry
+ ℌ.Definable fun v ↦ ∀ x < f v, P v x := by
+ rcases hf.bounded with ⟨bf, hbf⟩
+ have ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_db6a2c2b28b6_1 | fe26f38c05477fe9 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Arithmetic/Definability/BoundedDefinable.lean | BoundedDefinable | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 6 | [
{
"theorem_name": "ball_blt",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hf.bounded with ⟨bf, hbf⟩\n have : ℌ.Definable fun v ↦ ∃ x ≤ bf.val v id, x = f v ∧ ∀ y < x, P v y := by\n apply bexs';... | [
{
"name": "of_iff",
"text": "lemma of_iff {f g : (Fin k → V) → V} (H : DefinableBoundedFunction f) (h : ∀ v, f v = g v) : DefinableBoundedFunction g := by\n have : f = g := by funext v; simp [h]\n rcases this; exact H\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 196,
"n_subproofs": 1,
"... | [
{
"name": "bcomp₁",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 5,
"n_chars": 233,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}
] | 4 | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | @@ -140,19 +140,51 @@
lemma ball_blt {P : (Fin k → V) → V → Prop} {f : (Fin k → V) → V}
(hf : DefinableBoundedFunction f) (h : ℌ.Definable fun w ↦ P (w ·.succ) (w 0)) :
- ℌ.Definable fun v ↦ ∀ x < f v, P v x := sorry
+ ℌ.Definable fun v ↦ ∀ x < f v, P v x := by
+ rcases hf.bounded with ⟨bf, hbf⟩
+ have ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_db6a2c2b28b6_2 | 8e4eef0defaad5c3 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Arithmetic/Definability/BoundedDefinable.lean | BoundedDefinable | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 6 | [
{
"theorem_name": "ball_blt",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hf.bounded with ⟨bf, hbf⟩\n have : ℌ.Definable fun v ↦ ∃ x ≤ bf.val v id, x = f v ∧ ∀ y < x, P v y := by\n apply bexs';... | [
{
"name": "of_iff",
"text": "lemma of_iff {f g : (Fin k → V) → V} (H : DefinableBoundedFunction f) (h : ∀ v, f v = g v) : DefinableBoundedFunction g := by\n have : f = g := by funext v; simp [h]\n rcases this; exact H\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 196,
"n_subproofs": 1,
"... | [
{
"name": "bcomp₂",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 358,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}
] | 4 | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | @@ -140,19 +140,51 @@
lemma ball_blt {P : (Fin k → V) → V → Prop} {f : (Fin k → V) → V}
(hf : DefinableBoundedFunction f) (h : ℌ.Definable fun w ↦ P (w ·.succ) (w 0)) :
- ℌ.Definable fun v ↦ ∀ x < f v, P v x := sorry
+ ℌ.Definable fun v ↦ ∀ x < f v, P v x := by
+ rcases hf.bounded with ⟨bf, hbf⟩
+ have ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_db6a2c2b28b6_3 | b2adb689a187a081 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Arithmetic/Definability/BoundedDefinable.lean | BoundedDefinable | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 6 | [
{
"theorem_name": "ball_blt",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hf.bounded with ⟨bf, hbf⟩\n have : ℌ.Definable fun v ↦ ∃ x ≤ bf.val v id, x = f v ∧ ∀ y < x, P v y := by\n apply bexs';... | [
{
"name": "of_iff",
"text": "lemma of_iff {f g : (Fin k → V) → V} (H : DefinableBoundedFunction f) (h : ∀ v, f v = g v) : DefinableBoundedFunction g := by\n have : f = g := by funext v; simp [h]\n rcases this; exact H\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 196,
"n_subproofs": 1,
"... | [
{
"name": "bcomp₃",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 7,
"n_chars": 431,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}
] | 4 | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | @@ -140,19 +140,51 @@
lemma ball_blt {P : (Fin k → V) → V → Prop} {f : (Fin k → V) → V}
(hf : DefinableBoundedFunction f) (h : ℌ.Definable fun w ↦ P (w ·.succ) (w 0)) :
- ℌ.Definable fun v ↦ ∀ x < f v, P v x := sorry
+ ℌ.Definable fun v ↦ ∀ x < f v, P v x := by
+ rcases hf.bounded with ⟨bf, hbf⟩
+ have ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_db6a2c2b28b6_4 | d46a4991f9807b6e | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Arithmetic/Definability/BoundedDefinable.lean | BoundedDefinable | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 6 | [
{
"theorem_name": "ball_blt",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hf.bounded with ⟨bf, hbf⟩\n have : ℌ.Definable fun v ↦ ∃ x ≤ bf.val v id, x = f v ∧ ∀ y < x, P v y := by\n apply bexs';... | [
{
"name": "of_iff",
"text": "lemma of_iff {f g : (Fin k → V) → V} (H : DefinableBoundedFunction f) (h : ∀ v, f v = g v) : DefinableBoundedFunction g := by\n have : f = g := by funext v; simp [h]\n rcases this; exact H\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 196,
"n_subproofs": 1,
"... | [
{
"name": "bcomp₄",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 7,
"n_chars": 497,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}
] | 4 | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | module
public import Foundation.FirstOrder.Arithmetic.Definability.Definable
@[expose] public section
namespace LO.FirstOrder.Arithmetic
open PeanoMinus
variable {ξ : Type*} {n : ℕ}
variable {V : Type*} [ORingStructure V]
variable {ℌ : HierarchySymbol} {Γ Γ' : SigmaPiDelta}
variable (ℌ)
class Bounded (f : (Fin ... | @@ -140,19 +140,51 @@
lemma ball_blt {P : (Fin k → V) → V → Prop} {f : (Fin k → V) → V}
(hf : DefinableBoundedFunction f) (h : ℌ.Definable fun w ↦ P (w ·.succ) (w 0)) :
- ℌ.Definable fun v ↦ ∀ x < f v, P v x := sorry
+ ℌ.Definable fun v ↦ ∀ x < f v, P v x := by
+ rcases hf.bounded with ⟨bf, hbf⟩
+ have ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_1fc565a59a93_0 | abd75979da7a2079 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Calculus.lean | Calculus | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "unprovable_def",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Entailment.Unprovable; simp [provable_def]",
"n_chars": 55,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "provable_def",
"text": "lemma provable_def (φ : Proposition L) : 𝐋𝐊¹ ⊢ φ ↔ Nonempty (⊢ᴸᴷ¹ [φ]) := by rfl\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 103,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,... | [
{
"name": "unprovable_def",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 152,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | module
/- public import Foundation.Logic.Calculus -/
public import Foundation.Logic.Calculus
public import Foundation.Propositional.Entailment.AxiomEFQ
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Mathlib.Data.List.MinMax
/-! # One-sided sequent calculus for first-order classical logic -/
@[exp... | module
/- public import Foundation.Logic.Calculus -/
public import Foundation.Logic.Calculus
public import Foundation.Propositional.Entailment.AxiomEFQ
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Mathlib.Data.List.MinMax
/-! # One-sided sequent calculus for first-order classical logic -/
@[exp... | @@ -263,8 +263,11 @@
namespace LK.Proof
-lemma unprovable_def (φ : Proposition L) : 𝐋𝐊¹ ⊬ φ ↔ IsEmpty (⊢ᴸᴷ¹ [φ]) := sorry
+lemma provable_def (φ : Proposition L) : 𝐋𝐊¹ ⊢ φ ↔ Nonempty (⊢ᴸᴷ¹ [φ]) := by rfl
+lemma unprovable_def (φ : Proposition L) : 𝐋𝐊¹ ⊬ φ ↔ IsEmpty (⊢ᴸᴷ¹ [φ]) := by
+ unfold Entailment.Unp... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_1fc565a59a93_1 | 1dcca0c7f59b3ade | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Calculus.lean | Calculus | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "specialize",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply of_LK_provable\n refine ⟨?_⟩\n let φt : Sentence L := Semiformula.subst φ ![t]\n have d : ⊢ᴸᴷ¹ [∼(φt : Proposition L),... | [
{
"name": "of_LK_provable",
"text": "lemma of_LK_provable {T : Theory L} {φ : Sentence L} : 𝐋𝐊¹ ⊢ (φ : Proposition L) → T ⊢ φ := fun h ↦\n have : pullback 𝐋𝐊¹[L] (Rewriting.emb : Sentence L → Proposition L) ⊢ φ := h\n OneSidedLK.ContextualEntailment.of_principal_provable this\n\n",
"fan_in": 1,
... | [
{
"name": "specialize",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 766,
"n_subproofs": 3,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": ... | 1 | module
/- public import Foundation.Logic.Calculus -/
public import Foundation.Logic.Calculus
public import Foundation.Propositional.Entailment.AxiomEFQ
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Mathlib.Data.List.MinMax
/-! # One-sided sequent calculus for first-order classical logic -/
@[exp... | module
/- public import Foundation.Logic.Calculus -/
public import Foundation.Logic.Calculus
public import Foundation.Propositional.Entailment.AxiomEFQ
public import Foundation.FirstOrder.Basic.Syntax.Rew
public import Mathlib.Data.List.MinMax
/-! # One-sided sequent calculus for first-order classical logic -/
@[exp... | @@ -330,8 +330,21 @@
open Entailment Derivation
+lemma of_LK_provable {T : Theory L} {φ : Sentence L} : 𝐋𝐊¹ ⊢ (φ : Proposition L) → T ⊢ φ := fun h ↦
+ have : pullback 𝐋𝐊¹[L] (Rewriting.emb : Sentence L → Proposition L) ⊢ φ := h
+ OneSidedLK.ContextualEntailment.of_principal_provable this
+
lemma specialize ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ab7e5c5b1ce8_0 | de5c70c21e47ca04 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Operator.lean | Operator | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "positive_operator_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [Positive, bv_operator] using ⟨fun h i hi x hx ↦ h x i hi hx, fun h x i hi hx ↦ h i hi x hx⟩",
"n_chars": 1... | [
{
"name": "bv_operator",
"text": "lemma bv_operator {k} (o : Operator L k) (v : Fin k → Semiterm L ξ (n + 1)) :\n (o.operator v).bv = .biUnion o.term.bv fun i ↦ (v i).bv := by\n simp only [operator]\n generalize o.term = s\n induction s\n case bvar => simp\n case fvar => contradiction\n case func ... | [
{
"name": "positive_operator_iff",
"fan_in": 5,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 275,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_ne... | 1 | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | @@ -46,8 +46,18 @@
def bvar (x : Fin n) : Operator L n := ⟨#x⟩
+lemma bv_operator {k} (o : Operator L k) (v : Fin k → Semiterm L ξ (n + 1)) :
+ (o.operator v).bv = .biUnion o.term.bv fun i ↦ (v i).bv := by
+ simp only [operator]
+ generalize o.term = s
+ induction s
+ case bvar => simp
+ case fvar => cont... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ab7e5c5b1ce8_1 | 03c2d19b97524edf | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Operator.lean | Operator | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "positive_const",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by simp [const, positive_operator_iff]",
"n_chars": 39,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_... | [
{
"name": "positive_operator_iff",
"text": "lemma positive_operator_iff {k} {o : Operator L k} {v : Fin k → Semiterm L ξ (n + 1)} :\n (o.operator v).Positive ↔ ∀ i ∈ o.term.bv, (v i).Positive := by\n simpa [Positive, bv_operator] using ⟨fun h i hi x hx ↦ h x i hi hx, fun h x i hi hx ↦ h i hi x hx⟩\n\n",... | [
{
"name": "positive_const",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 4,
"n_chars": 201,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 2 | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | @@ -55,8 +55,12 @@
case fvar => contradiction
case func => simp [Rew.func, bv_func, Finset.biUnion_biUnion, *]
-@[simp] lemma positive_const (c : Const L) : (c : Semiterm L ξ (n + 1)).Positive := sorry
+lemma positive_operator_iff {k} {o : Operator L k} {v : Fin k → Semiterm L ξ (n + 1)} :
+ (o.operator v).P... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ab7e5c5b1ce8_2 | 3ac9d1f75213d664 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Operator.lean | Operator | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "numeral_add_two",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n numeral_succ (by simp)",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation":... | [
{
"name": "numeral_succ",
"text": "lemma numeral_succ (hz : z ≠ 0) : numeral L (z + 1) = Operator.Add.add.comp ![numeral L z, One.one] := by\n simp [numeral]\n cases' z with z\n · simp at hz\n · rfl\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": 5,
... | [
{
"name": "numeral_add_two",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 125,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 1 | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | @@ -156,8 +156,15 @@
variable [hz : Operator.Zero L] [ho : Operator.One L] [ha : Operator.Add L]
-lemma numeral_add_two : numeral L (z + 2) = Operator.Add.add.comp ![numeral L (z + 1), One.one] := sorry
+lemma numeral_succ (hz : z ≠ 0) : numeral L (z + 1) = Operator.Add.add.comp ![numeral L z, One.one] := by
+ si... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ab7e5c5b1ce8_3 | b4497c0824948725 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Operator.lean | Operator | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "finitary0",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by simp [ω.operator', Matrix.empty_eq]",
"n_chars": 40,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "operator'",
"text": "protected lemma operator' (o : Semiterm.Operator L k) (v : Fin k → Semiterm L ξ₁ n₁) :\n ω (o.operator v) = o.operator (ω ∘ v) := ω.operator o v\n\n",
"fan_in": 4,
"n_lines": 4,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "finitary0",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 175,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 1
... | 1 | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | @@ -412,17 +412,20 @@
· simp [comp_app]
· contradiction
+protected lemma operator' (o : Semiterm.Operator L k) (v : Fin k → Semiterm L ξ₁ n₁) :
+ ω (o.operator v) = o.operator (ω ∘ v) := ω.operator o v
+
@[simp] lemma finitary0 (o : Semiterm.Operator L 0) (v : Fin 0 → Semiterm L ξ₁ n₁) :
- ω (o.operator ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ab7e5c5b1ce8_4 | 6a2ee3eaf2c35c22 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Operator.lean | Operator | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "hom_operator'",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " ω.hom_operator o v",
"n_chars": 20,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"... | [
{
"name": "hom_operator",
"text": "lemma hom_operator (o : Semiformula.Operator L k) (v : Fin k → Semiterm L ξ₁ n₁) :\n ω ▹ o.operator v = o.operator fun i ↦ ω (v i) := by\n unfold Semiformula.Operator.operator Rewriting.subst Rewriting.emb\n simp only [← TransitiveRewriting.comp_app]; congr 2\n ext\n... | [
{
"name": "hom_operator'",
"fan_in": 5,
"n_deps_direct": 3,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 1 | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | @@ -429,8 +429,16 @@
@[simp] protected lemma const (c : Semiterm.Const L) : ω c = c := by simp [Semiterm.Operator.const]
+lemma hom_operator (o : Semiformula.Operator L k) (v : Fin k → Semiterm L ξ₁ n₁) :
+ ω ▹ o.operator v = o.operator fun i ↦ ω (v i) := by
+ unfold Semiformula.Operator.operator Rewriting.sub... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_ab7e5c5b1ce8_5 | 9d3f61bcc5ede595 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Basic/Operator.lean | Operator | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "hom_finitary0",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by simp [ω.hom_operator', Matrix.empty_eq]",
"n_chars": 44,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "hom_operator'",
"text": "lemma hom_operator' (o : Semiformula.Operator L k) (v : Fin k → Semiterm L ξ₁ n₁) :\n ω ▹ o.operator v = o.operator (ω ∘ v) := ω.hom_operator o v\n\n",
"fan_in": 5,
"n_lines": 4,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,... | [
{
"name": "hom_finitary0",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 190,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 2 | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | module
public import Foundation.FirstOrder.Basic.Semantics.Semantics
@[expose] public section
namespace LO
namespace FirstOrder
variable {L : Language}
namespace Semiterm
structure Operator (L : Language) (n : ℕ) where
term : ClosedSemiterm L n
abbrev Const (L : Language.{u}) := Operator L 0
def fn {k} (f : ... | @@ -437,19 +437,23 @@
· simp [Rew.comp_app]
· contradiction
+lemma hom_operator' (o : Semiformula.Operator L k) (v : Fin k → Semiterm L ξ₁ n₁) :
+ ω ▹ o.operator v = o.operator (ω ∘ v) := ω.hom_operator o v
+
@[simp] lemma hom_finitary0 (o : Semiformula.Operator L 0) (v : Fin 0 → Semiterm L ξ₁ n₁) :
- ω ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_0 | 1dab100055b7b373 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "not_meaningful_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by simp [meaningful_iff]",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation... | [
{
"name": "meaningful_iff",
"text": "lemma meaningful_iff {𝓜 : M} : Meaningful 𝓜 ↔ ∃ φ, 𝓜 ⊭ φ :=\n ⟨by rintro ⟨h⟩; exact h, fun h ↦ ⟨h⟩⟩\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 132,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,... | [
{
"name": "not_meaningful_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 3,
"n_chars": 109,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 1 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -149,8 +149,11 @@
instance [LogicalConnective F] [Semantics.Bot M] (𝓜 : M) : Meaningful 𝓜 := ⟨⟨⊥, by grind⟩⟩
-lemma not_meaningful_iff (𝓜 : M) : ¬Meaningful 𝓜 ↔ ∀ φ, 𝓜 ⊧ φ := sorry
+lemma meaningful_iff {𝓜 : M} : Meaningful 𝓜 ↔ ∃ φ, 𝓜 ⊭ φ :=
+ ⟨by rintro ⟨h⟩; exact h, fun h ↦ ⟨h⟩⟩
+lemma not_meaningf... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_1 | b7f8c12044fc2e2c | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 9 | [
{
"theorem_name": "not_satisfiable_finset",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Satisfiable, modelsSet_iff, Valid];",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "modelsSet_iff",
"text": "lemma modelsSet_iff {𝓜 : M} {T : Set F} : 𝓜 ⊧* T ↔ ∀ ⦃φ⦄, φ ∈ T → Models 𝓜 φ :=\n ⟨by rintro ⟨h⟩ φ hf; exact h hf, by intro h; exact ⟨h⟩⟩\n\n",
"fan_in": 9,
"n_lines": 4,
"n_chars": 178,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n... | [
{
"name": "not_satisfiable_finset",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 213,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_n... | 1 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -149,18 +149,24 @@
instance [LogicalConnective F] [Semantics.Bot M] (𝓜 : M) : Meaningful 𝓜 := ⟨⟨⊥, by grind⟩⟩
+lemma modelsSet_iff {𝓜 : M} {T : Set F} : 𝓜 ⊧* T ↔ ∀ ⦃φ⦄, φ ∈ T → Models 𝓜 φ :=
+ ⟨by rintro ⟨h⟩ φ hf; exact h hf, by intro h; exact ⟨h⟩⟩
+
@[simp] lemma modelsTheory_theory (𝓜 : M) : 𝓜 ⊧* the... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_2 | cf44d9526a7b80e1 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 9 | [
{
"theorem_name": "not_satisfiable_finset",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Satisfiable, modelsSet_iff, Valid];",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "modelsSet_iff",
"text": "lemma modelsSet_iff {𝓜 : M} {T : Set F} : 𝓜 ⊧* T ↔ ∀ ⦃φ⦄, φ ∈ T → Models 𝓜 φ :=\n ⟨by rintro ⟨h⟩ φ hf; exact h hf, by intro h; exact ⟨h⟩⟩\n\n",
"fan_in": 9,
"n_lines": 4,
"n_chars": 178,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n... | [
{
"name": "satisfiable_conj₂",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 200,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nestin... | 1 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -149,15 +149,20 @@
instance [LogicalConnective F] [Semantics.Bot M] (𝓜 : M) : Meaningful 𝓜 := ⟨⟨⊥, by grind⟩⟩
+lemma modelsSet_iff {𝓜 : M} {T : Set F} : 𝓜 ⊧* T ↔ ∀ ⦃φ⦄, φ ∈ T → Models 𝓜 φ :=
+ ⟨by rintro ⟨h⟩ φ hf; exact h hf, by intro h; exact ⟨h⟩⟩
+
@[simp] lemma modelsTheory_theory (𝓜 : M) : 𝓜 ⊧* the... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_3 | 0a280223969fe5dd | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "meaningful_iff_satisfiableSet",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [set_meaningful_iff_nonempty, satisfiableSet_iff_models_nonempty]",
"n_chars": 76,
"n_subproofs"... | [
{
"name": "set_meaningful_iff_nonempty",
"text": "lemma set_meaningful_iff_nonempty [LogicalConnective F] [∀ 𝓜 : M, Meaningful 𝓜] {s : Set M} : Meaningful s ↔ s.Nonempty := by\n constructor;\n . rintro ⟨φ, hf⟩;\n by_contra A;\n rcases Set.not_nonempty_iff_eq_empty.mp A; simp [NotModels] at hf;\n ... | [
{
"name": "meaningful_iff_satisfiableSet",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 4,
"n_lines": 4,
"n_chars": 216,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 2 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -225,8 +225,18 @@
instance [LogicalConnective F] [Semantics.Top M] : Semantics.Top (Set M) := ⟨fun s ↦ by simp [set_models_iff]⟩
-lemma meaningful_iff_satisfiableSet [LogicalConnective F] [∀ 𝓜 : M, Meaningful 𝓜] : Satisfiable M T ↔ Meaningful (models M T) := sorry
+lemma set_meaningful_iff_nonempty [LogicalCo... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_4 | 5f5a60a07fedde05 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "consequence_iff'",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨fun h _ _ => consequence_iff.mp h inferInstance, fun H 𝓜 hs => @H 𝓜 hs⟩",
"n_chars": 85,
"n_subproofs": 0,
"n_... | [
{
"name": "consequence_iff",
"text": "lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := iff_of_eq rfl\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 119,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "consequence_iff'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 195,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -221,8 +221,11 @@
instance [LogicalConnective F] [Semantics.Top M] : Semantics.Top (Set M) := ⟨fun s ↦ by simp [set_models_iff]⟩
-lemma consequence_iff' {T : Set F} {φ : F} : T ⊨[M] φ ↔ (∀ (𝓜 : M) [𝓜 ⊧* T], 𝓜 ⊧ φ) := sorry
+lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := if... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_5 | 8915aeefe9bb52c4 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "consequence_iff'",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨fun h _ _ => consequence_iff.mp h inferInstance, fun H 𝓜 hs => @H 𝓜 hs⟩",
"n_chars": 85,
"n_subproofs": 0,
"n_... | [
{
"name": "consequence_iff",
"text": "lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := iff_of_eq rfl\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 119,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "consequence_iff_not_satisfiable",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 411,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,... | 1 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -221,8 +221,15 @@
instance [LogicalConnective F] [Semantics.Top M] : Semantics.Top (Set M) := ⟨fun s ↦ by simp [set_models_iff]⟩
+lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := iff_of_eq rfl
+
lemma consequence_iff_not_satisfiable [LogicalConnective F] [Tarski M] {φ : F} :
-... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_6 | 7ccd17d9923635d6 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "consequence_iff'",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨fun h _ _ => consequence_iff.mp h inferInstance, fun H 𝓜 hs => @H 𝓜 hs⟩",
"n_chars": 85,
"n_subproofs": 0,
"n_... | [
{
"name": "consequence_iff",
"text": "lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := iff_of_eq rfl\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 119,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "weakening",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 167,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -227,8 +227,11 @@
instance [LogicalConnective F] [Semantics.Top M] : Semantics.Top (Set M) := ⟨fun s ↦ by simp [set_models_iff]⟩
-lemma weakening {T U : Set F} {φ} (h : T ⊨[M] φ) (ss : T ⊆ U) : U ⊨[M] φ := sorry
+lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := iff_of_eq rfl
... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_7 | ebc9118ad8278fb7 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "finset_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n haveI := Classical.decEq\n induction u using Finset.induction\n case empty => exact ⟨0, by simp⟩\n case insert φ u _ ih =>\n... | [
{
"name": "subset_of_le",
"text": "lemma subset_of_le {T : ℕ → Set F} (H : Cumulative T)\n {s₁ s₂ : ℕ} (h : s₁ ≤ s₂) : T s₁ ⊆ T s₂ := by\n suffices ∀ s d, T s ⊆ T (s + d) by\n simpa [Nat.add_sub_of_le h] using this s₁ (s₂ - s₁)\n intro s d\n induction' d with d ih\n · simp\n · simpa only [Nat.add... | [
{
"name": "finset_mem",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 738,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 4,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nesting": ... | 1 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -230,6 +230,15 @@
namespace Cumulative
+lemma subset_of_le {T : ℕ → Set F} (H : Cumulative T)
+ {s₁ s₂ : ℕ} (h : s₁ ≤ s₂) : T s₁ ⊆ T s₂ := by
+ suffices ∀ s d, T s ⊆ T (s + d) by
+ simpa [Nat.add_sub_of_le h] using this s₁ (s₂ - s₁)
+ intro s d
+ induction' d with d ih
+ · simp
+ · simpa only [Nat.ad... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_8 | 14dbdab1534acc67 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "consequence_iff'",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨fun h _ _ => consequence_iff.mp h inferInstance, fun H 𝓜 hs => @H 𝓜 hs⟩",
"n_chars": 85,
"n_subproofs": 0,
"n_... | [
{
"name": "consequence_iff",
"text": "lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := iff_of_eq rfl\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 119,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "conseq_compact",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 794,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max_nestin... | 2 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -227,8 +227,15 @@
instance [LogicalConnective F] [Semantics.Top M] : Semantics.Top (Set M) := ⟨fun s ↦ by simp [set_models_iff]⟩
+lemma consequence_iff {T : Set F} {φ} : T ⊨[M] φ ↔ ∀ {𝓜 : M}, 𝓜 ⊧* T → 𝓜 ⊧ φ := iff_of_eq rfl
+
lemma consequence_iff_not_satisfiable [LogicalConnective F] [Tarski M] {φ : F} :
-... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_53c903925395_9 | 309b424885c461ad | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Logic/Semantics.lean | Semantics | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "compact_cumulative",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨by intro H s\n exact H.of_subset (Set.subset_iUnion T s),\n by intro H\n apply compact.mpr\n intro u hu\n... | [
{
"name": "finset_mem",
"text": "lemma finset_mem {T : ℕ → Set F}\n (H : Cumulative T) {u : Finset F} (hu : ↑u ⊆ ⋃ s, T s) : ∃ s, ↑u ⊆ T s := by\n haveI := Classical.decEq\n induction u using Finset.induction\n case empty => exact ⟨0, by simp⟩\n case insert φ u _ ih =>\n have hu : insert φ ↑u ⊆ ⋃ ... | [
{
"name": "compact_cumulative",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 357,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max_nes... | 2 | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | module
public import Foundation.Logic.LogicSymbol
/-!
# Basic definitions and properties of semantics-related notions
This file defines the semantics of formulas based on Tarski's truth definitions.
Also provides 𝓜 characterization of compactness.
## Main Definitions
* `LO.Semantics`: The realization of 𝓜 formula.... | @@ -245,6 +245,22 @@
· simp
· simpa only [Nat.add_succ, add_zero] using subset_trans ih (H (s + d))
+lemma finset_mem {T : ℕ → Set F}
+ (H : Cumulative T) {u : Finset F} (hu : ↑u ⊆ ⋃ s, T s) : ∃ s, ↑u ⊆ T s := by
+ haveI := Classical.decEq
+ induction u using Finset.induction
+ case empty => exact ⟨0, by ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_1f0ef23e7718_0 | 0241063c2a7af247 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Arithmetic/HFS/Fixpoint.lean | Fixpoint | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "succ_existsUnique",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have : 𝚺₁-Predicate fun x ↦ x ≤ s ∧ c.Φ v {z | z ∈ ih} x := by\n apply HierarchySymbol.Definable.and (by definability... | [
{
"name": "eval_formula",
"text": "lemma eval_formula (v : Fin k.succ.succ → V) :\n φ.core.val.Evalb v ↔ c.Φ (v ·.succ.succ) {x | x ∈ v 1} (v 0) := c.defined.iff\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 139,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation":... | [
{
"name": "succ_existsUnique",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 531,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nest... | 1 | module
public import Foundation.FirstOrder.Arithmetic.HFS.PRF
@[expose] public section
/-!
# Fixpoint Construction
-/
namespace LO.FirstOrder.Arithmetic
variable {V : Type*} [ORingStructure V] [V↓[ℒₒᵣ] ⊧* 𝗜𝚺₁]
namespace Fixpoint
structure Blueprint (k : ℕ) where
core : 𝚫₁.Semisentence (k + 2)
namespace Bl... | module
public import Foundation.FirstOrder.Arithmetic.HFS.PRF
@[expose] public section
/-!
# Fixpoint Construction
-/
namespace LO.FirstOrder.Arithmetic
variable {V : Type*} [ORingStructure V] [V↓[ℒₒᵣ] ⊧* 𝗜𝚺₁]
namespace Fixpoint
structure Blueprint (k : ℕ) where
core : 𝚫₁.Semisentence (k + 2)
namespace Bl... | @@ -64,12 +64,15 @@
variable {k : ℕ} {φ : Blueprint k} (c : Construction V φ) (v : Fin k → V)
+lemma eval_formula (v : Fin k.succ.succ → V) :
+ φ.core.val.Evalb v ↔ c.Φ (v ·.succ.succ) {x | x ∈ v 1} (v 0) := c.defined.iff
+
lemma succ_existsUnique (s ih : V) :
∃! u : V, ∀ x, (x ∈ u ↔ x ≤ s ∧ c.Φ v {z | z ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_1f0ef23e7718_1 | 025554a4e419b04c | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Arithmetic/HFS/Fixpoint.lean | Fixpoint | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "eval_fixpointDef",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " c.fixpoint_defined.iff",
"n_chars": 23,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0... | [
{
"name": "fixpoint_defined",
"text": "lemma fixpoint_defined : 𝚺₁.Defined (fun v ↦ c.Fixpoint (v ·.succ) (v 0)) φ.fixpointDef := .mk fun v ↦ by\n simp [Blueprint.fixpointDef, c.eval_limSeqDef]; rfl\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 172,
"n_subproofs": 0,
"n_tactics": 3,
... | [
{
"name": "eval_fixpointDef",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 148,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | module
public import Foundation.FirstOrder.Arithmetic.HFS.PRF
@[expose] public section
/-!
# Fixpoint Construction
-/
namespace LO.FirstOrder.Arithmetic
variable {V : Type*} [ORingStructure V] [V↓[ℒₒᵣ] ⊧* 𝗜𝚺₁]
namespace Fixpoint
structure Blueprint (k : ℕ) where
core : 𝚫₁.Semisentence (k + 2)
namespace Bl... | module
public import Foundation.FirstOrder.Arithmetic.HFS.PRF
@[expose] public section
/-!
# Fixpoint Construction
-/
namespace LO.FirstOrder.Arithmetic
variable {V : Type*} [ORingStructure V] [V↓[ℒₒᵣ] ⊧* 𝗜𝚺₁]
namespace Fixpoint
structure Blueprint (k : ℕ) where
core : 𝚫₁.Semisentence (k + 2)
namespace Bl... | @@ -231,8 +231,11 @@
section
+lemma fixpoint_defined : 𝚺₁.Defined (fun v ↦ c.Fixpoint (v ·.succ) (v 0)) φ.fixpointDef := .mk fun v ↦ by
+ simp [Blueprint.fixpointDef, c.eval_limSeqDef]; rfl
+
@[simp] lemma eval_fixpointDef (v : Fin (k + 1) → V) :
- φ.fixpointDef.val.Evalb v ↔ c.Fixpoint (v ·.succ) (v 0) := s... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_92a703e76b8a_0 | ecdb1496d30b629b | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Bootstrapping/Syntax/Formula/Typed.lean | Typed | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ext",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_inj.mp h",
"n_chars": 13,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "val_inj",
"text": "lemma val_inj {φ ψ : Semiformula V L n} :\n φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_str... | [
{
"name": "ext",
"fan_in": 56,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 3,
"n_chars": 94,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1
}
] | 1 | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | @@ -93,8 +93,11 @@
@[simp] lemma val_iff (φ ψ : Semiformula V L n) :
(φ 🡘 ψ).val = iff L φ.val ψ.val := rfl
-@[ext] lemma ext {φ ψ : Semiformula V L n} (h : φ.val = ψ.val) : φ = ψ := sorry
+lemma val_inj {φ ψ : Semiformula V L n} :
+ φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp
+@[ext] lemma ext {... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_92a703e76b8a_1 | 8d7feb83ccade448 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Bootstrapping/Syntax/Formula/Typed.lean | Typed | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ext",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_inj.mp h",
"n_chars": 13,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "val_inj",
"text": "lemma val_inj {φ ψ : Semiformula V L n} :\n φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_str... | [
{
"name": "shift_substs",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 213,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | @@ -93,8 +93,11 @@
@[simp] lemma val_iff (φ ψ : Semiformula V L n) :
(φ 🡘 ψ).val = iff L φ.val ψ.val := rfl
-@[ext] lemma ext {φ ψ : Semiformula V L n} (h : φ.val = ψ.val) : φ = ψ := sorry
+lemma val_inj {φ ψ : Semiformula V L n} :
+ φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp
+@[ext] lemma ext {... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_92a703e76b8a_2 | 6fd16bd10a194bd8 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Bootstrapping/Syntax/Formula/Typed.lean | Typed | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ext",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_inj.mp h",
"n_chars": 13,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "val_inj",
"text": "lemma val_inj {φ ψ : Semiformula V L n} :\n φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_str... | [
{
"name": "substs_substs",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 273,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 1 | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | @@ -93,8 +93,11 @@
@[simp] lemma val_iff (φ ψ : Semiformula V L n) :
(φ 🡘 ψ).val = iff L φ.val ψ.val := rfl
-@[ext] lemma ext {φ ψ : Semiformula V L n} (h : φ.val = ψ.val) : φ = ψ := sorry
+lemma val_inj {φ ψ : Semiformula V L n} :
+ φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp
+@[ext] lemma ext {... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_92a703e76b8a_3 | e9b04d792c4800d9 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Bootstrapping/Syntax/Formula/Typed.lean | Typed | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ext",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_inj.mp h",
"n_chars": 13,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "val_inj",
"text": "lemma val_inj {φ ψ : Semiformula V L n} :\n φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_str... | [
{
"name": "neg_ball",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 204,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | @@ -93,8 +93,11 @@
@[simp] lemma val_iff (φ ψ : Semiformula V L n) :
(φ 🡘 ψ).val = iff L φ.val ψ.val := rfl
-@[ext] lemma ext {φ ψ : Semiformula V L n} (h : φ.val = ψ.val) : φ = ψ := sorry
+lemma val_inj {φ ψ : Semiformula V L n} :
+ φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp
+@[ext] lemma ext {... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_92a703e76b8a_4 | 3e129e9406a6c0b0 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Bootstrapping/Syntax/Formula/Typed.lean | Typed | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ext",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_inj.mp h",
"n_chars": 13,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "val_inj",
"text": "lemma val_inj {φ ψ : Semiformula V L n} :\n φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_str... | [
{
"name": "neg_bexs",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 204,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | @@ -93,8 +93,11 @@
@[simp] lemma val_iff (φ ψ : Semiformula V L n) :
(φ 🡘 ψ).val = iff L φ.val ψ.val := rfl
-@[ext] lemma ext {φ ψ : Semiformula V L n} (h : φ.val = ψ.val) : φ = ψ := sorry
+lemma val_inj {φ ψ : Semiformula V L n} :
+ φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp
+@[ext] lemma ext {... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_92a703e76b8a_5 | 1ab03f91ece4774f | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/FirstOrder/Bootstrapping/Syntax/Formula/Typed.lean | Typed | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ext",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_inj.mp h",
"n_chars": 13,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "val_inj",
"text": "lemma val_inj {φ ψ : Semiformula V L n} :\n φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_str... | [
{
"name": "Semiformula.ball_eqss_imp",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 205,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"ma... | 2 | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | module
public import Foundation.FirstOrder.Bootstrapping.Syntax.Term.Typed
public import Foundation.FirstOrder.Bootstrapping.Syntax.Formula.Iteration
@[expose] public section
/-!
# Typed Formalized Semiformula/Formula
-/
namespace LO.FirstOrder.Arithmetic.Bootstrapping
variable {V : Type*} [ORingStructure V] [V↓[ℒₒ... | @@ -93,8 +93,11 @@
@[simp] lemma val_iff (φ ψ : Semiformula V L n) :
(φ 🡘 ψ).val = iff L φ.val ψ.val := rfl
-@[ext] lemma ext {φ ψ : Semiformula V L n} (h : φ.val = ψ.val) : φ = ψ := sorry
+lemma val_inj {φ ψ : Semiformula V L n} :
+ φ.val = ψ.val ↔ φ = ψ := by rcases φ; rcases ψ; simp
+@[ext] lemma ext {... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_375ef45787e8_0 | 6dc27f3d57e9af3d | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Heyting/Semantics.lean | Semantics | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "sound",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rintro ⟨d⟩;\n apply mod_models_iff.mpr;\n intro ℍ hℍ;\n induction d with\n | axm hφ => apply hℍ.models_set; assumption;\n | @md... | [
{
"name": "mod_models_iff",
"text": "lemma mod_models_iff {φ : Formula α} :\n mod.{_,w} H ⊧ φ ↔ ∀ ℍ : HeytingSemantics.{_,w} α, ℍ ⊧* H → ℍ ⊧ φ := by\n simp [mod, Semantics.models, Semantics.set_models_iff]\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 195,
"n_subproofs": 0,
"n_tactics"... | [
{
"name": "sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 426,
"n_subproofs": 1,
"n_tactics": 16,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"max_nesting": 4
}... | 2 | module
public import Foundation.Propositional.Hilbert.Minimal.Basic
public import Foundation.Logic.LindenbaumAlgebra
public import Foundation.Vorspiel.Order.Heyting
@[expose] public section
namespace LO.Propositional
variable {α : Type u}
namespace Formula
def hVal {ℍ : Type*} [HeytingAlgebra ℍ] (v : α → ℍ) : For... | module
public import Foundation.Propositional.Hilbert.Minimal.Basic
public import Foundation.Logic.LindenbaumAlgebra
public import Foundation.Vorspiel.Order.Heyting
@[expose] public section
namespace LO.Propositional
variable {α : Type u}
namespace Formula
def hVal {ℍ : Type*} [HeytingAlgebra ℍ] (v : α → ℍ) : For... | @@ -96,8 +96,21 @@
variable {H : Hilbert α}
-lemma sound {φ : Formula α} : H ⊢ φ → mod H ⊧ φ := sorry
+lemma mod_models_iff {φ : Formula α} :
+ mod.{_,w} H ⊧ φ ↔ ∀ ℍ : HeytingSemantics.{_,w} α, ℍ ⊧* H → ℍ ⊧ φ := by
+ simp [mod, Semantics.models, Semantics.set_models_iff]
+lemma sound {φ : Formula α} : H ⊢ φ ... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_375ef45787e8_1 | 08152cb3cb51627a | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Propositional/Heyting/Semantics.lean | Semantics | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "sound",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rintro ⟨d⟩;\n apply mod_models_iff.mpr;\n intro ℍ hℍ;\n induction d with\n | axm hφ => apply hℍ.models_set; assumption;\n | @md... | [
{
"name": "val_def'",
"text": "lemma val_def' {ℍ : HeytingSemantics α} {φ : Formula α} : ℍ ⊧ φ ↔ (ℍ ⊧ₕ φ) = ⊤ := by rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 111,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": ... | [
{
"name": "lindenbaum_complete_iff",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 5,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max... | 2 | module
public import Foundation.Propositional.Hilbert.Minimal.Basic
public import Foundation.Logic.LindenbaumAlgebra
public import Foundation.Vorspiel.Order.Heyting
@[expose] public section
namespace LO.Propositional
variable {α : Type u}
namespace Formula
def hVal {ℍ : Type*} [HeytingAlgebra ℍ] (v : α → ℍ) : For... | module
public import Foundation.Propositional.Hilbert.Minimal.Basic
public import Foundation.Logic.LindenbaumAlgebra
public import Foundation.Vorspiel.Order.Heyting
@[expose] public section
namespace LO.Propositional
variable {α : Type u}
namespace Formula
def hVal {ℍ : Type*} [HeytingAlgebra ℍ] (v : α → ℍ) : For... | @@ -75,6 +75,8 @@
lemma val_def {ℍ : HeytingSemantics α} {φ : Formula α} : ℍ ⊧ φ ↔ φ.hVal ℍ.valAtom = ⊤ := by rfl
+lemma val_def' {ℍ : HeytingSemantics α} {φ : Formula α} : ℍ ⊧ φ ↔ (ℍ ⊧ₕ φ) = ⊤ := by rfl
+
instance : Semantics.Top (HeytingSemantics α) := ⟨fun ℍ ↦ by simp [val_def]⟩
instance : Semantics.Bot (He... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_c9e9d75d2f5b_0 | 1af1fc5d39cfa0c3 | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Syntax/Predicate/Rew.lean | Rew | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "q_comp_bShift_app",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := ext' (ω.q_comp_bShift) t; simpa only [comp_app] using this",
"n_chars": 73,
"n_subproofs": 1,
"n_tact... | [
{
"name": "ext'",
"text": "lemma ext' {ω₁ ω₂ : Rew L ξ₁ n₁ ξ₂ n₂} (h : ω₁ = ω₂) (t) : ω₁ t = ω₂ t := by simp [h]\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 115,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
... | [
{
"name": "q_comp_bShift_app",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 4,
"n_chars": 171,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | module
public import Foundation.Syntax.Predicate.Quantifier
public import Foundation.Syntax.Predicate.Term
public import Foundation.Vorspiel.Function
/-!
# Rewriting
term/formula morphisms such as Rewritings, substitutions, and embs are handled by the structure `LO.FirstOrder.Rew`.
- `LO.FirstOrder.Rew.rewrite f` is... | module
public import Foundation.Syntax.Predicate.Quantifier
public import Foundation.Syntax.Predicate.Term
public import Foundation.Vorspiel.Function
/-!
# Rewriting
term/formula morphisms such as Rewritings, substitutions, and embs are handled by the structure `LO.FirstOrder.Rew`.
- `LO.FirstOrder.Rew.rewrite f` is... | @@ -49,6 +49,8 @@
apply DFunLike.ext ω₁ ω₂; intro t
induction t <;> simp [*, ω₁.func, ω₂.func, Function.comp_def]
+lemma ext' {ω₁ ω₂ : Rew L ξ₁ n₁ ξ₂ n₂} (h : ω₁ = ω₂) (t) : ω₁ t = ω₂ t := by simp [h]
+
protected def id : Rew L ξ n ξ n where
toFun := id
func'' := fun _ _ => rfl
@@ -298,7 +300,8 @@
@[sim... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
ablate_c9e9d75d2f5b_1 | 0a1206ffac1e3fcd | lean | lean | github.com/FormalizedFormalLogic/Foundation | 87d4dd68835a6c1eb8448b9c392d9ca51fe08d63 | Foundation/Syntax/Predicate/Rew.lean | Rew | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "qpow_comp",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction k <;> simp [*, q_comp]",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_autom... | [
{
"name": "q_comp",
"text": "lemma q_comp (ω₂ : Rew L ξ₂ n₂ ξ₃ n₃) (ω₁ : Rew L ξ₁ n₁ ξ₂ n₂) :\n (Rew.comp ω₂ ω₁).q = ω₂.q.comp ω₁.q := by\n ext x\n · cases x using Fin.cases <;> simp [comp_app]\n · simp [comp_app]\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 228,
"n_subproofs": 0,
"... | [
{
"name": "qpow_comp",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 5,
"n_chars": 211,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | module
public import Foundation.Syntax.Predicate.Quantifier
public import Foundation.Syntax.Predicate.Term
public import Foundation.Vorspiel.Function
/-!
# Rewriting
term/formula morphisms such as Rewritings, substitutions, and embs are handled by the structure `LO.FirstOrder.Rew`.
- `LO.FirstOrder.Rew.rewrite f` is... | module
public import Foundation.Syntax.Predicate.Quantifier
public import Foundation.Syntax.Predicate.Term
public import Foundation.Vorspiel.Function
/-!
# Rewriting
term/formula morphisms such as Rewritings, substitutions, and embs are handled by the structure `LO.FirstOrder.Rew`.
- `LO.FirstOrder.Rew.rewrite f` is... | @@ -324,8 +324,15 @@
@[simp] lemma qpow_id {k} : (Rew.id : Rew L ξ n ξ n).qpow k = Rew.id := by induction k <;> simp [*]
+lemma q_comp (ω₂ : Rew L ξ₂ n₂ ξ₃ n₃) (ω₁ : Rew L ξ₁ n₁ ξ₂ n₂) :
+ (Rew.comp ω₂ ω₁).q = ω₂.q.comp ω₁.q := by
+ ext x
+ · cases x using Fin.cases <;> simp [comp_app]
+ · simp [comp_app]
+
... | {
"repo": "Foundation",
"git_repo": "github.com/FormalizedFormalLogic/Foundation",
"revision": "87d4dd68835a6c1eb8448b9c392d9ca51fe08d63",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--cor... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.