module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Algebra.GroupWithZero.Associated | {
"line": 250,
"column": 20
} | {
"line": 250,
"column": 28
} | [
{
"pp": "M : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\np : M\nn : ℕ\nhp : Prime (p ^ n)\nthis : n = 1\n⊢ Prime p ∧ n = 1",
"usedConstants": [
"congrArg",
"and_self",
"Prime",
"Eq.mp",
"id",
"instOfNatNat",
"CommMonoidWithZero.toMonoidWithZe... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.GroupWithZero.Associated | {
"line": 657,
"column": 2
} | {
"line": 658,
"column": 54
} | [
{
"pp": "M : Type u_1\ninst✝ : CommMonoidWithZero M\na b : M\n⊢ DvdNotUnit (Associates.mk a) (Associates.mk b) ↔ DvdNotUnit a b",
"usedConstants": [
"Associated.comm",
"CommMonoidWithZero.toCommMonoid",
"Monoid",
"Eq.mpr",
"Associates.mk",
"_private.Mathlib.Algebra.GroupW... | simp only [DvdNotUnit, mk_ne_zero, mk_surjective.exists, isUnit_mk, mk_mul_mk,
mk_eq_mk_iff_associated, Associated.comm (x := b)] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Algebra.Equiv | {
"line": 411,
"column": 4
} | {
"line": 411,
"column": 44
} | [
{
"pp": "R : Type uR\nA₁ : Type uA₁\nA₂ : Type uA₂\nA₃ : Type uA₃\nA₁' : Type uA₁'\nA₂' : Type uA₂'\nA₃' : Type uA₃'\ninst✝¹² : CommSemiring R\ninst✝¹¹ : Semiring A₁\ninst✝¹⁰ : Semiring A₂\ninst✝⁹ : Semiring A₃\ninst✝⁸ : Semiring A₁'\ninst✝⁷ : Semiring A₂'\ninst✝⁶ : Semiring A₃'\ninst✝⁵ : Algebra R A₁\ninst✝⁴ :... | simp only [AlgHom.comp_assoc, symm_comp] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Ring.Subring.Basic | {
"line": 1146,
"column": 4
} | {
"line": 1146,
"column": 62
} | [
{
"pp": "case a\nR : Type u\nS : Type v\ninst✝¹ : NonAssocRing R\ninst✝ : NonAssocRing S\nf : R →+* S\ns : Subring R\nx y : R\nhy : y ∈ s\nhxy : x - y ∈ ⇑f ⁻¹' {0}\n⊢ x ∈ s ⊔ closure (⇑f ⁻¹' {0})",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Subring.instSetLike",
"Compl... | rw [← closure_eq s, ← closure_union, ← add_sub_cancel y x] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Module.Submodule.Range | {
"line": 333,
"column": 2
} | {
"line": 333,
"column": 10
} | [
{
"pp": "case a\nR : Type u_1\nM : Type u_5\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nN₁ N₂ N : Submodule R M\nh₁ : N₁ ≤ N\nh₂ : N₂ ≤ N\n⊢ N.subtype.range ⊓ (N₁ ⊔ N₂) = map N.subtype (comap N.subtype N₁ ⊔ comap N.subtype N₂)",
"usedConstants": [
"Submodule",
"RingHomSur... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finset.Lattice.Prod | {
"line": 55,
"column": 80
} | {
"line": 55,
"column": 88
} | [
{
"pp": "ι : Type u_7\nκ : Type u_8\nα : Type u_9\nβ : Type u_10\ninst✝³ : SemilatticeSup α\ninst✝² : SemilatticeSup β\ninst✝¹ : OrderBot α\ninst✝ : OrderBot β\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → β\ni : α × β\na : ι\nha : a ∈ s\nb : κ\nhb : b ∈ t\n⊢ ((∀ b ∈ s, f b ≤ i.1) ∧ ∀ b ∈ t, g b ≤ i.2) → ∀ (a... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finset.Lattice.Prod | {
"line": 55,
"column": 80
} | {
"line": 55,
"column": 88
} | [
{
"pp": "ι : Type u_7\nκ : Type u_8\nα : Type u_9\nβ : Type u_10\ninst✝³ : SemilatticeSup α\ninst✝² : SemilatticeSup β\ninst✝¹ : OrderBot α\ninst✝ : OrderBot β\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → β\ni : α × β\na : ι\nha : a ∈ s\nb : κ\nhb : b ∈ t\n⊢ ((∀ b ∈ s, f b ≤ i.1) ∧ ∀ b ∈ t, g b ≤ i.2) → ∀ (a... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Lattice.Prod | {
"line": 55,
"column": 80
} | {
"line": 55,
"column": 88
} | [
{
"pp": "ι : Type u_7\nκ : Type u_8\nα : Type u_9\nβ : Type u_10\ninst✝³ : SemilatticeSup α\ninst✝² : SemilatticeSup β\ninst✝¹ : OrderBot α\ninst✝ : OrderBot β\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → β\ni : α × β\na : ι\nha : a ∈ s\nb : κ\nhb : b ∈ t\n⊢ ((∀ b ∈ s, f b ≤ i.1) ∧ ∀ b ∈ t, g b ≤ i.2) → ∀ (a... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Lattice.Prod | {
"line": 101,
"column": 14
} | {
"line": 101,
"column": 22
} | [
{
"pp": "ι : Type u_7\nκ : Type u_8\nα : Type u_9\nβ : Type u_10\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup β\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → β\ni : α × β\na : ι\nha : a ∈ s\nb : κ\nhb : b ∈ t\n⊢ ((∀ b ∈ s, f b ≤ i.1) ∧ ∀ b ∈ t, g b ≤ i.2) → ∀ (a : ι) (b : κ), a ∈ s → b ∈ t → f a ≤ i.1 ∧... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finset.Lattice.Prod | {
"line": 101,
"column": 14
} | {
"line": 101,
"column": 22
} | [
{
"pp": "ι : Type u_7\nκ : Type u_8\nα : Type u_9\nβ : Type u_10\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup β\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → β\ni : α × β\na : ι\nha : a ∈ s\nb : κ\nhb : b ∈ t\n⊢ ((∀ b ∈ s, f b ≤ i.1) ∧ ∀ b ∈ t, g b ≤ i.2) → ∀ (a : ι) (b : κ), a ∈ s → b ∈ t → f a ≤ i.1 ∧... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Lattice.Prod | {
"line": 101,
"column": 14
} | {
"line": 101,
"column": 22
} | [
{
"pp": "ι : Type u_7\nκ : Type u_8\nα : Type u_9\nβ : Type u_10\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup β\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → β\ni : α × β\na : ι\nha : a ∈ s\nb : κ\nhb : b ∈ t\n⊢ ((∀ b ∈ s, f b ≤ i.1) ∧ ∀ b ∈ t, g b ≤ i.2) → ∀ (a : ι) (b : κ), a ∈ s → b ∈ t → f a ≤ i.1 ∧... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Closure | {
"line": 76,
"column": 84
} | {
"line": 76,
"column": 92
} | [
{
"pp": "case e_IsClosed.h.a\nα : Type u_1\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : Preorder α\ntoOrderHom✝ : α →o α\nle_closure'✝¹ : ∀ (x : α), x ≤ toOrderHom✝.toFun x\nidempotent'✝¹ : ∀ (x : α), toOrderHom✝.toFun (toOrderHom✝.toFun x) = toOrderHom✝.toFun x\nIsClosed✝¹ : α → Prop\nisClosed_iff✝¹ : ∀ {x : α}, I... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.LinearAlgebra.Span.Defs | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 14
} | [
{
"pp": "M : Type u_4\ninst✝ : AddCommMonoid M\ns : Set M\n⊢ span ℕ s ≤ AddSubmonoid.toNatSubmodule.symm.symm (AddSubmonoid.closure s)",
"usedConstants": [
"Eq.mpr",
"Submodule",
"AddSubmonoid.toNatSubmodule",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreord... | rw [span_le] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Span.Defs | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 14
} | [
{
"pp": "R : Type u_1\nM : Type u_4\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set (Set M)\n⊢ span R (⋃₀ s) ≤ sSup (span R '' s)",
"usedConstants": [
"Eq.mpr",
"Submodule",
"congrArg",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"S... | rw [span_le] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Module.Submodule.Pointwise | {
"line": 444,
"column": 2
} | {
"line": 445,
"column": 49
} | [
{
"pp": "R : Type u_2\nM : Type u_3\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nS : Type u_4\ninst✝² : Monoid S\ninst✝¹ : DistribMulAction S M\nN : Submodule R M\ninst✝ : SMulCommClass S R M\na : S\np : (x : M) → x ∈ a • N → Prop\nsmul₀ : ∀ (s : M) (hs : s ∈ N), p (a • s) ⋯\nx : M\nhx :... | let p' (x : M) (hx : x ∈ ({a} : Set S) • N) : Prop :=
p x (by rwa [← Submodule.singleton_set_smul]) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.LinearAlgebra.Span.Defs | {
"line": 338,
"column": 2
} | {
"line": 338,
"column": 14
} | [
{
"pp": "R : Type u_1\nM : Type u_4\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set M\nr : R\n⊢ span R (r • s) ≤ span R s",
"usedConstants": [
"Eq.mpr",
"Submodule",
"instHSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZer... | rw [span_le] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Span.Defs | {
"line": 498,
"column": 6
} | {
"line": 498,
"column": 22
} | [
{
"pp": "R : Type u_1\nM : Type u_4\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nx : M\nr : Rˣ\n⊢ R ∙ ↑r • x = R ∙ x",
"usedConstants": [
"Units.val",
"Eq.mpr",
"Submodule",
"instHSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid... | ← Units.smul_def | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Span.Defs | {
"line": 614,
"column": 23
} | {
"line": 614,
"column": 31
} | [
{
"pp": "R : Type u_1\nM : Type u_4\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set M\na : M\nt : Finset M\nhat : a ∉ t\nIH : ↑t ⊆ ↑(span R s) → ∃ T, ↑T ⊆ s ∧ ↑t ⊆ ↑(span R ↑T)\nht : ↑(insert a t) ⊆ ↑(span R s)\nT : Finset M\nhTs : ↑T ⊆ s\nhtT : ↑t ⊆ ↑(span R ↑T)\nT' : Finset M\nhT's... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.LinearAlgebra.Span.Defs | {
"line": 614,
"column": 23
} | {
"line": 614,
"column": 31
} | [
{
"pp": "R : Type u_1\nM : Type u_4\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set M\na : M\nt : Finset M\nhat : a ∉ t\nIH : ↑t ⊆ ↑(span R s) → ∃ T, ↑T ⊆ s ∧ ↑t ⊆ ↑(span R ↑T)\nht : ↑(insert a t) ⊆ ↑(span R s)\nT : Finset M\nhTs : ↑T ⊆ s\nhtT : ↑t ⊆ ↑(span R ↑T)\nT' : Finset M\nhT's... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Span.Defs | {
"line": 614,
"column": 23
} | {
"line": 614,
"column": 31
} | [
{
"pp": "R : Type u_1\nM : Type u_4\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set M\na : M\nt : Finset M\nhat : a ∉ t\nIH : ↑t ⊆ ↑(span R s) → ∃ T, ↑T ⊆ s ∧ ↑t ⊆ ↑(span R ↑T)\nht : ↑(insert a t) ⊆ ↑(span R s)\nT : Finset M\nhTs : ↑T ⊆ s\nhtT : ↑t ⊆ ↑(span R ↑T)\nT' : Finset M\nhT's... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Atoms | {
"line": 593,
"column": 6
} | {
"line": 593,
"column": 14
} | [
{
"pp": "case inl\nι : Sort u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : OrderBot α\ninst✝ : IsAtomistic α\nb : α\nhsb : IsLUB ∅ b\nhs : ∀ a ∈ ∅, IsAtom a\n⊢ b = ⊥ ∨ ∃ a, IsAtom a ∧ a ≤ b",
"usedConstants": [
"congrArg",
"true_or",
"OrderBot.toBot",
"PartialOrde... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Atoms | {
"line": 593,
"column": 6
} | {
"line": 593,
"column": 14
} | [
{
"pp": "case inl\nι : Sort u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : OrderBot α\ninst✝ : IsAtomistic α\nb : α\nhsb : IsLUB ∅ b\nhs : ∀ a ∈ ∅, IsAtom a\n⊢ b = ⊥ ∨ ∃ a, IsAtom a ∧ a ≤ b",
"usedConstants": [
"congrArg",
"true_or",
"OrderBot.toBot",
"PartialOrde... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Atoms | {
"line": 593,
"column": 6
} | {
"line": 593,
"column": 14
} | [
{
"pp": "case inl\nι : Sort u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : OrderBot α\ninst✝ : IsAtomistic α\nb : α\nhsb : IsLUB ∅ b\nhs : ∀ a ∈ ∅, IsAtom a\n⊢ b = ⊥ ∨ ∃ a, IsAtom a ∧ a ≤ b",
"usedConstants": [
"congrArg",
"true_or",
"OrderBot.toBot",
"PartialOrde... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Atoms | {
"line": 602,
"column": 73
} | {
"line": 604,
"column": 77
} | [
{
"pp": "α : Type u_2\ninst✝² : PartialOrder α\ninst✝¹ : OrderBot α\ninst✝ : IsAtomistic α\nb : α\n⊢ IsLUB {a | IsAtom a ∧ a ≤ b} b",
"usedConstants": [
"lowerBounds",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"IsAtomistic.isLU... | by
rcases isLUB_atoms b with ⟨s, hsb, hs⟩
exact ⟨fun c hc ↦ hc.2, fun c hc ↦ hsb.2 fun i hi ↦ hc ⟨hs _ hi, hsb.1 hi⟩⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Atoms | {
"line": 615,
"column": 6
} | {
"line": 615,
"column": 22
} | [
{
"pp": "α : Type u_2\ninst✝² : PartialOrder α\ninst✝¹ : OrderBot α\ninst✝ : IsAtomistic α\na b : α\nh : ∀ (c : α), IsAtom c → (c ≤ a ↔ c ≤ b)\n⊢ a = b",
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"LE.le",
"And",
... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Atoms | {
"line": 616,
"column": 2
} | {
"line": 616,
"column": 10
} | [
{
"pp": "α : Type u_2\ninst✝² : PartialOrder α\ninst✝¹ : OrderBot α\ninst✝ : IsAtomistic α\na b : α\nh : ∀ (c : α), IsAtom c → (c ≤ a ↔ c ≤ b)\n⊢ (∀ (c : α), IsAtom c → c ≤ a → c ≤ b) ∧ ∀ (c : α), IsAtom c → c ≤ b → c ≤ a",
"usedConstants": [
"congrArg",
"and_self",
"PartialOrder.toPreorde... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Atoms | {
"line": 633,
"column": 6
} | {
"line": 633,
"column": 14
} | [
{
"pp": "case inl\nι : Sort u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : OrderTop α\ninst✝ : IsCoatomistic α\nb : α\nhsb : IsGLB ∅ b\nhs : ∀ a ∈ ∅, IsCoatom a\n⊢ b = ⊤ ∨ ∃ a, IsCoatom a ∧ b ≤ a",
"usedConstants": [
"congrArg",
"true_or",
"PartialOrder.toPreorder",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Atoms | {
"line": 633,
"column": 6
} | {
"line": 633,
"column": 14
} | [
{
"pp": "case inl\nι : Sort u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : OrderTop α\ninst✝ : IsCoatomistic α\nb : α\nhsb : IsGLB ∅ b\nhs : ∀ a ∈ ∅, IsCoatom a\n⊢ b = ⊤ ∨ ∃ a, IsCoatom a ∧ b ≤ a",
"usedConstants": [
"congrArg",
"true_or",
"PartialOrder.toPreorder",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Atoms | {
"line": 633,
"column": 6
} | {
"line": 633,
"column": 14
} | [
{
"pp": "case inl\nι : Sort u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : OrderTop α\ninst✝ : IsCoatomistic α\nb : α\nhsb : IsGLB ∅ b\nhs : ∀ a ∈ ∅, IsCoatom a\n⊢ b = ⊤ ∨ ∃ a, IsCoatom a ∧ b ≤ a",
"usedConstants": [
"congrArg",
"true_or",
"PartialOrder.toPreorder",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Atoms | {
"line": 904,
"column": 6
} | {
"line": 906,
"column": 23
} | [
{
"pp": "case refine_1\nι : Sort u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : Lattice α\ninst✝¹ : BoundedOrder α\ninst✝ : IsSimpleOrder α\ns : Set α\nx : α\nh : x ∈ s\n⊢ x ≤ if ⊤ ∈ s then ⊤ else ⊥",
"usedConstants": [
"Eq.mpr",
"Lattice",
"le_refl",
"Lattice.toSemilatticeSup",
"co... | · rcases eq_bot_or_eq_top x with (rfl | rfl)
· exact bot_le
· rw [if_pos h] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Order.Atoms | {
"line": 1118,
"column": 4
} | {
"line": 1118,
"column": 89
} | [
{
"pp": "α : Type u_2\ninst✝³ : Lattice α\ninst✝² : OrderBot α\ninst✝¹ : IsUpperModularLattice α\ninst✝ : IsAtomistic α\na b : α\nhab : a < b\ns : Set α\nhsb : IsLUB s b\nh : ∀ a ∈ s, IsAtom a\nx : α\nhx : x ∈ s\nhcon : ¬a ⋖ x ⊔ a\n⊢ x ≤ a",
"usedConstants": [
"congrArg",
"and_self",
"Orde... | obtain (hbot | h_inf) := (h x hx).bot_covBy.eq_or_eq (c := x ⊓ a) (by simp) (by simp) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Order.SupIndep | {
"line": 247,
"column": 2
} | {
"line": 248,
"column": 41
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝³ : Lattice α\ninst✝² : IsModularLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq ι\ns t : Finset ι\nf : ι → α\nhs : s.SupIndep f\nht : t.SupIndep f\nh : Disjoint (s.sup f) (t.sup f)\n⊢ (s ∪ t).SupIndep f",
"usedConstants": [
"Eq.mpr",
"Finset.instUni... | rw [show s ∪ t = ({s, t} : Finset _).biUnion id by simp]
grind [SupIndep.biUnion, supIndep_pair] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SupIndep | {
"line": 247,
"column": 2
} | {
"line": 248,
"column": 41
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝³ : Lattice α\ninst✝² : IsModularLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq ι\ns t : Finset ι\nf : ι → α\nhs : s.SupIndep f\nht : t.SupIndep f\nh : Disjoint (s.sup f) (t.sup f)\n⊢ (s ∪ t).SupIndep f",
"usedConstants": [
"Eq.mpr",
"Finset.instUni... | rw [show s ∪ t = ({s, t} : Finset _).biUnion id by simp]
grind [SupIndep.biUnion, supIndep_pair] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SupIndep | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝ : CompleteLattice α\na i : α\nhi : i ∈ {a}\n⊢ Disjoint i (sSup ({a} \\ {i}))",
"usedConstants": [
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"sSup_empty",
"CompleteLattice.toLattice",
"congrArg",
"OrderBot.t... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.SupIndep | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝ : CompleteLattice α\na i : α\nhi : i ∈ {a}\n⊢ Disjoint i (sSup ({a} \\ {i}))",
"usedConstants": [
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"sSup_empty",
"CompleteLattice.toLattice",
"congrArg",
"OrderBot.t... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SupIndep | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝ : CompleteLattice α\na i : α\nhi : i ∈ {a}\n⊢ Disjoint i (sSup ({a} \\ {i}))",
"usedConstants": [
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"sSup_empty",
"CompleteLattice.toLattice",
"congrArg",
"OrderBot.t... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SupIndep | {
"line": 297,
"column": 76
} | {
"line": 298,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝ : CompleteLattice α\na i : α\nhi : i ∈ {a}\n⊢ Disjoint i (sSup ({a} \\ {i}))",
"usedConstants": [
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"sSup_empty",
"CompleteLattice.toLattice",
"congrArg",
"OrderBot.t... | by
simp_all | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.SupIndep | {
"line": 419,
"column": 2
} | {
"line": 419,
"column": 10
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝ : CompleteLattice α\nβ : ι → Type u_5\nt : (i : ι) → β i → α\nht : ∀ (i : ι), iSupIndep (t i)\nb₁ : (i : ι) → β i\nhb₁ : b₁ ∈ {b | ⨅ i, t i (b i) ≠ ⊥}\nb₂ : (i : ι) → β i\nhb₂ : b₂ ∈ {b | ⨅ i, t i (b i) ≠ ⊥}\nh_eq : ⨅ i, t i (b₁ i) = ⨅ i, t i (b₂ i)\nh_ne : ¬b₁ = b₂\ni... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.SupIndep | {
"line": 423,
"column": 2
} | {
"line": 423,
"column": 10
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝ : CompleteLattice α\nt : ι → α\nht : iSupIndep t\nh_ne_bot : ∀ (i : ι), t i ≠ ⊥\n⊢ univ = {i | t i ≠ ⊥}",
"usedConstants": [
"False",
"Lattice.toSemilatticeSup",
"eq_false",
"CompleteLattice.toLattice",
"congrArg",
"Set.univ",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Notation.Indicator | {
"line": 160,
"column": 21
} | {
"line": 160,
"column": 29
} | [
{
"pp": "case pos\nα : Type u_1\nβ : Type u_2\nM : Type u_3\ninst✝ : One M\ns : Set α\nf : α → M\na : α\nt : Set β\ng : β → M\nb : β\nh1 : a ∈ s ↔ b ∈ t\nh2 : f a = g b\nh✝ : a ∈ s\n⊢ s.mulIndicator f a = t.mulIndicator g b",
"usedConstants": [
"congrArg",
"Set.mulIndicator",
"true_iff",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Notation.Indicator | {
"line": 160,
"column": 21
} | {
"line": 160,
"column": 29
} | [
{
"pp": "case neg\nα : Type u_1\nβ : Type u_2\nM : Type u_3\ninst✝ : One M\ns : Set α\nf : α → M\na : α\nt : Set β\ng : β → M\nb : β\nh1 : a ∈ s ↔ b ∈ t\nh2 : f a = g b\nh✝ : ¬a ∈ s\n⊢ s.mulIndicator f a = t.mulIndicator g b",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"Set.... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.GroupWithZero.Finset | {
"line": 54,
"column": 64
} | {
"line": 58,
"column": 81
} | [
{
"pp": "ι : Type u_1\nM₀ : Type u_4\ninst✝² : CommMonoidWithZero M₀\nf : ι → M₀\ns : Finset ι\ninst✝¹ : Nontrivial M₀\ninst✝ : NoZeroDivisors M₀\n⊢ ∏ x ∈ s, f x = 0 ↔ ∃ a ∈ s, f a = 0",
"usedConstants": [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"MulOne.toOne",
"False",
"N... | by
classical
induction s using Finset.induction_on with
| empty => exact ⟨Not.elim one_ne_zero, fun ⟨_, H, _⟩ => by simp at H⟩
| insert _ _ ha ih => rw [prod_insert ha, mul_eq_zero, exists_mem_insert, ih] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.BigOperators.Pi | {
"line": 120,
"column": 48
} | {
"line": 120,
"column": 56
} | [
{
"pp": "case intro.h\nI : Type u_7\ninst✝³ : DecidableEq I\nM : I → Type u_8\ninst✝² : (i : I) → CommMonoid (M i)\ninst✝¹ : Finite I\nN : Type u_9\ninst✝ : CommMonoid N\ng h : ((i : I) → M i) →* N\nH : ∀ (i : I) (x : M i), g (Pi.mulSingle i x) = h (Pi.mulSingle i x)\nval✝ : Fintype I\nk : (i : I) → M i\n⊢ ∏ x,... | map_prod | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Multiset.Antidiagonal | {
"line": 83,
"column": 10
} | {
"line": 83,
"column": 19
} | [
{
"pp": "case cons\nα : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nhs : s.antidiagonal = map (fun t ↦ (s - t, t)) s.powerset\n⊢ map (fun x ↦ (s - x, a ::ₘ x)) s.powerset + map (fun x ↦ (a ::ₘ (s - x), x)) s.powerset =\n map (fun x ↦ (a ::ₘ s - x, x)) s.powerset + map (fun x ↦ (a ::ₘ s - a ::ₘ x,... | sub_cons, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.CompactlyGenerated.Basic | {
"line": 668,
"column": 4
} | {
"line": 668,
"column": 12
} | [
{
"pp": "case refine_2.refine_1\nα : Type u_2\ninst✝² : CompleteLattice α\ninst✝¹ : IsModularLattice α\ninst✝ : IsCompactlyGenerated α\nb c : α\nhbc : b ≤ c\nh : sSup {a | a ≤ c ∧ IsAtom a} = c\ns : Set α\ns_max : ∀ ⦃t : Set α⦄, t ∈ {s | sSupIndep s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a ∧ a ≤ c} → s ⊆ t → s... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.CompactlyGenerated.Basic | {
"line": 668,
"column": 4
} | {
"line": 668,
"column": 12
} | [
{
"pp": "case refine_2.refine_1\nα : Type u_2\ninst✝² : CompleteLattice α\ninst✝¹ : IsModularLattice α\ninst✝ : IsCompactlyGenerated α\nb c : α\nhbc : b ≤ c\nh : sSup {a | a ≤ c ∧ IsAtom a} = c\ns : Set α\ns_max : ∀ ⦃t : Set α⦄, t ∈ {s | sSupIndep s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a ∧ a ≤ c} → s ⊆ t → s... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.CompactlyGenerated.Basic | {
"line": 668,
"column": 4
} | {
"line": 668,
"column": 12
} | [
{
"pp": "case refine_2.refine_1\nα : Type u_2\ninst✝² : CompleteLattice α\ninst✝¹ : IsModularLattice α\ninst✝ : IsCompactlyGenerated α\nb c : α\nhbc : b ≤ c\nh : sSup {a | a ≤ c ∧ IsAtom a} = c\ns : Set α\ns_max : ∀ ⦃t : Set α⦄, t ∈ {s | sSupIndep s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a ∧ a ≤ c} → s ⊆ t → s... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Span.Basic | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 15
} | [
{
"pp": "R : Type u_1\nM : Type u_4\nS : Type u_7\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : Semiring S\ninst✝² : SMul R S\ninst✝¹ : Module S M\ninst✝ : IsScalarTower R S M\np : Submodule R M\nq : Submodule S M\nh₁ : p ≤ restrictScalars R q\nh₂ : q ≤ span S ↑p\n⊢ map q.subtype... | rw [map_span] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Group.Indicator | {
"line": 132,
"column": 8
} | {
"line": 132,
"column": 36
} | [
{
"pp": "case pos\nα : Type u_1\nM : Type u_4\ninst✝¹ : MulOneClass M\ns : Set α\ninst✝ : DecidablePred fun x ↦ x ∈ s\nf g : α → M\nx : α\nh : x ∈ s\n⊢ (s.mulIndicator f * sᶜ.mulIndicator g) x = s.piecewise f g x",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"congrArg",... | piecewise_eq_of_mem _ _ _ h, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Finsupp.Defs | {
"line": 357,
"column": 74
} | {
"line": 357,
"column": 82
} | [
{
"pp": "α : Type u_1\nM : Type u_4\nN : Type u_5\ninst✝¹ : Zero M\ninst✝ : Zero N\ne : M → N\nhe₀ : e 0 = 0\ng : α →₀ N\nf : α → M\nh : ∀ (i : α), e (f i) = g i\n⊢ ∀ (a : α), (fun x ↦ if x ∈ g.support then f x else 0) a ≠ 0 → a ∈ g.support",
"usedConstants": [
"Finsupp.instFunLike",
"instDecida... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finsupp.Defs | {
"line": 357,
"column": 74
} | {
"line": 357,
"column": 82
} | [
{
"pp": "α : Type u_1\nM : Type u_4\nN : Type u_5\ninst✝¹ : Zero M\ninst✝ : Zero N\ne : M → N\nhe₀ : e 0 = 0\ng : α →₀ N\nf : α → M\nh : ∀ (i : α), e (f i) = g i\n⊢ ∀ (a : α), (fun x ↦ if x ∈ g.support then f x else 0) a ≠ 0 → a ∈ g.support",
"usedConstants": [
"Finsupp.instFunLike",
"instDecida... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finsupp.Defs | {
"line": 357,
"column": 74
} | {
"line": 357,
"column": 82
} | [
{
"pp": "α : Type u_1\nM : Type u_4\nN : Type u_5\ninst✝¹ : Zero M\ninst✝ : Zero N\ne : M → N\nhe₀ : e 0 = 0\ng : α →₀ N\nf : α → M\nh : ∀ (i : α), e (f i) = g i\n⊢ ∀ (a : α), (fun x ↦ if x ∈ g.support then f x else 0) a ≠ 0 → a ∈ g.support",
"usedConstants": [
"Finsupp.instFunLike",
"instDecida... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Span.Basic | {
"line": 610,
"column": 6
} | {
"line": 610,
"column": 10
} | [
{
"pp": "R : Type u_1\nR₂ : Type u_2\nM : Type u_4\nM₂ : Type u_5\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring R₂\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : AddCommGroup M₂\ninst✝¹ : Module R₂ M₂\nτ₁₂ : R →+* R₂\ninst✝ : RingHomSurjective τ₁₂\nf : M →ₛₗ[τ₁₂] M₂\nS : Submodule R M\nhf : f.range = ⊤\n⊢ (f... | ← hf | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Group.Finsupp | {
"line": 63,
"column": 53
} | {
"line": 63,
"column": 61
} | [
{
"pp": "case inl\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ng₁ g₂ : ι →₀ M\ninst✝ : DecidableEq ι\nh : Disjoint g₁.support g₂.support\na : ι\nha : a ∈ g₁.support ∪ g₂.support\nh✝ : a ∈ g₁.support ∧ a ∉ g₂.support\n⊢ a ∈ (g₁ + g₂).support",
"usedConstants": [
"Finsupp.instFunLike",
"F... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Group.Finsupp | {
"line": 63,
"column": 53
} | {
"line": 63,
"column": 61
} | [
{
"pp": "case inr\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ng₁ g₂ : ι →₀ M\ninst✝ : DecidableEq ι\nh : Disjoint g₁.support g₂.support\na : ι\nha : a ∈ g₁.support ∪ g₂.support\nh✝ : a ∈ g₂.support ∧ a ∉ g₁.support\n⊢ a ∈ (g₁ + g₂).support",
"usedConstants": [
"Finsupp.instFunLike",
"F... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.LinearAlgebra.Span.Basic | {
"line": 676,
"column": 43
} | {
"line": 676,
"column": 60
} | [
{
"pp": "K : Type u_3\nV : Type u_6\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nx : V\ns q : Submodule K V\nhpq : s < q\nhqp : q < K ∙ x ⊔ s\nc : K\nz : V\nhz : z ∈ s\nhyq : c • x ∈ q\nhyp : c • x + z ∉ s\nhc : c ≠ 0\n⊢ x ∈ q",
"usedConstants": [
"Submodule",
"instHSMu... | q.smul_mem_iff hc | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Group.Finsupp | {
"line": 189,
"column": 8
} | {
"line": 189,
"column": 16
} | [
{
"pp": "case neg\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ninst✝ : DecidableEq ι\nf g : ι →₀ M\nh : ∀ x ∈ f.support ∩ g.support, AddCommute (f x) (g x)\nx : ι\nhf : x ∈ f.support\nhg : x ∉ g.support\n⊢ (f + g) x = (g + f) x",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Group.Finsupp | {
"line": 189,
"column": 8
} | {
"line": 189,
"column": 16
} | [
{
"pp": "case neg\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ninst✝ : DecidableEq ι\nf g : ι →₀ M\nh : ∀ x ∈ f.support ∩ g.support, AddCommute (f x) (g x)\nx : ι\nhf : x ∈ f.support\nhg : x ∉ g.support\n⊢ (f + g) x = (g + f) x",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Finsupp | {
"line": 189,
"column": 8
} | {
"line": 189,
"column": 16
} | [
{
"pp": "case neg\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ninst✝ : DecidableEq ι\nf g : ι →₀ M\nh : ∀ x ∈ f.support ∩ g.support, AddCommute (f x) (g x)\nx : ι\nhf : x ∈ f.support\nhg : x ∉ g.support\n⊢ (f + g) x = (g + f) x",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Finsupp | {
"line": 190,
"column": 6
} | {
"line": 190,
"column": 14
} | [
{
"pp": "case neg\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ninst✝ : DecidableEq ι\nf g : ι →₀ M\nh : ∀ x ∈ f.support ∩ g.support, AddCommute (f x) (g x)\nx : ι\nhf : x ∉ f.support\n⊢ (f + g) x = (g + f) x",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_not._simp_1",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Group.Finsupp | {
"line": 190,
"column": 6
} | {
"line": 190,
"column": 14
} | [
{
"pp": "case neg\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ninst✝ : DecidableEq ι\nf g : ι →₀ M\nh : ∀ x ∈ f.support ∩ g.support, AddCommute (f x) (g x)\nx : ι\nhf : x ∉ f.support\n⊢ (f + g) x = (g + f) x",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_not._simp_1",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Finsupp | {
"line": 190,
"column": 6
} | {
"line": 190,
"column": 14
} | [
{
"pp": "case neg\nι : Type u_1\nM : Type u_3\ninst✝¹ : AddZeroClass M\ninst✝ : DecidableEq ι\nf g : ι →₀ M\nh : ∀ x ∈ f.support ∩ g.support, AddCommute (f x) (g x)\nx : ι\nhf : x ∉ f.support\n⊢ (f + g) x = (g + f) x",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_not._simp_1",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Span.Basic | {
"line": 756,
"column": 83
} | {
"line": 757,
"column": 69
} | [
{
"pp": "R : Type u_1\nM : Type u_4\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nx : M\n⊢ toSpanSingleton R M x = 0 ↔ x = 0",
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"Function.Injective.eq... | by
rw [← toSpanSingleton_zero, (toSpanSingleton_injective R M).eq_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Group.Finsupp | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 10
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\ninst✝ : AddZeroClass M\nmotive : (ι →₀ M) → Prop\nf : ι →₀ M\nzero : motive 0\nadd_single : ∀ (a : ι) (b : M) (f : ι →₀ M), a ∉ f.support → b ≠ 0 → motive f → motive (f + single a b)\na✝⁵ : ι\na✝⁴ : M\na✝³ : ι →₀ M\na✝² : a✝⁵ ∉ a✝³.support\na✝¹ : a✝⁴ ≠ 0\na✝ : motive a✝³\n⊢ ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Group.Indicator | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 12
} | [
{
"pp": "case pos\nι : Sort u_1\nα : Type u_2\nM : Type u_3\ninst✝² : CompleteLattice M\ninst✝¹ : One M\ninst✝ : Nonempty ι\nh1 : ⊥ = 1\ns : ι → Set α\nf : α → M\nx : α\nhx : x ∈ ⋂ i, s i\n⊢ (⋂ i, s i).mulIndicator f x = ⨅ i, (s i).mulIndicator f x",
"usedConstants": [
"iInf",
"congrArg",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Group.Indicator | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 12
} | [
{
"pp": "case pos\nι : Sort u_1\nα : Type u_2\nM : Type u_3\ninst✝² : CompleteLattice M\ninst✝¹ : One M\ninst✝ : Nonempty ι\nh1 : ⊥ = 1\ns : ι → Set α\nf : α → M\nx : α\nhx : x ∈ ⋂ i, s i\n⊢ (⋂ i, s i).mulIndicator f x = ⨅ i, (s i).mulIndicator f x",
"usedConstants": [
"iInf",
"congrArg",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.Indicator | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 12
} | [
{
"pp": "case pos\nι : Sort u_1\nα : Type u_2\nM : Type u_3\ninst✝² : CompleteLattice M\ninst✝¹ : One M\ninst✝ : Nonempty ι\nh1 : ⊥ = 1\ns : ι → Set α\nf : α → M\nx : α\nhx : x ∈ ⋂ i, s i\n⊢ (⋂ i, s i).mulIndicator f x = ⨅ i, (s i).mulIndicator f x",
"usedConstants": [
"iInf",
"congrArg",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.Option | {
"line": 203,
"column": 38
} | {
"line": 203,
"column": 41
} | [
{
"pp": "case add\nα : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝¹ : AddZeroClass M\ninst✝ : CommMonoid N\nb : Option α → M → N\nh_zero : ∀ (o : Option α), b o 0 = 1\nh_add : ∀ (o : Option α) (m₁ m₂ : M), b o (m₁ + m₂) = b o m₁ * b o m₂\nf₁ f₂ : Option α →₀ M\nh₁ : f₁.prod b = b none (f₁ none) * f₁.some.prod f... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.FiniteSupport.Basic | {
"line": 192,
"column": 53
} | {
"line": 192,
"column": 61
} | [
{
"pp": "α : Type u_1\nM : Type u_4\ninst✝ : Monoid M\nf : α → M\ng : α → ℕ\nhg : HasFiniteSupport g\na : α\nha : a ∉ support g\n⊢ a ∉ mulSupport fun a ↦ f a ^ g a",
"usedConstants": [
"MulOne.toOne",
"False",
"Function.mem_mulSupport._simp_2",
"Function.mem_support._simp_1",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finsupp.Basic | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nN : Type u_16\ninst✝ : AddCommMonoid N\nf : α →₀ N\na : α\n⊢ (f.sum fun x v ↦ if a = x then v else 0) = f a",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_not._simp_1",
"congrArg",
"Finset",
"Finsupp.sum_ite_eq",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finsupp.Basic | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nN : Type u_16\ninst✝ : AddCommMonoid N\nf : α →₀ N\na : α\n⊢ (f.sum fun x v ↦ if a = x then v else 0) = f a",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_not._simp_1",
"congrArg",
"Finset",
"Finsupp.sum_ite_eq",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Finsupp.Basic | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nN : Type u_16\ninst✝ : AddCommMonoid N\nf : α →₀ N\na : α\n⊢ (f.sum fun x v ↦ if a = x then v else 0) = f a",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_not._simp_1",
"congrArg",
"Finset",
"Finsupp.sum_ite_eq",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.BigOperators.Finsupp.Basic | {
"line": 107,
"column": 48
} | {
"line": 108,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nN : Type u_16\ninst✝ : AddCommMonoid N\nf : α →₀ N\na : α\n⊢ (f.sum fun x v ↦ if a = x then v else 0) = f a",
"usedConstants": [
"Finsupp.instFunLike",
"Classical.not_not._simp_1",
"congrArg",
"Finset",
"Finsupp.sum_ite_eq",
... | by
simp_all | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.BigOperators.Finsupp.Basic | {
"line": 571,
"column": 2
} | {
"line": 572,
"column": 46
} | [
{
"pp": "α : Type u_1\nM : Type u_8\ninst✝ : AddCommMonoid M\ns : Finset α\nf : (a : α) → a ∈ s → M\n⊢ ∀ x ∈ s, x ∉ (indicator s f).support → single x ((indicator s f) x) = 0",
"usedConstants": [
"Finsupp.instFunLike",
"Finsupp.indicator",
"Eq.mpr",
"congrArg",
"Finsupp.notMem_... | · intro i _ hi
rw [notMem_support_iff.mp hi, single_zero] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Finsupp.Basic | {
"line": 148,
"column": 28
} | {
"line": 148,
"column": 79
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nM : Type u_5\nN : Type u_6\nP : Type u_7\nG : Type u_8\nH : Type u_9\nR : Type u_10\nS : Type u_11\ninst✝ : Zero M\nf : α ≃ β\nl : α →₀ M\na : β\n⊢ a ∈ map f.toEmbedding l.support ↔ l (f.symm a) ≠ 0",
"usedConstants": [
"Finsupp.instFunL... | simp only [Finset.mem_map_equiv, mem_support_toFun] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Finsupp.Basic | {
"line": 277,
"column": 31
} | {
"line": 277,
"column": 44
} | [
{
"pp": "case h₁\nα : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝ : AddCommMonoid M\nf : α → β\nhf : Injective f\nx : α →₀ M\na : α\na✝ : x a = 0\n⊢ 0 (f a) = 0",
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Pi.zero_apply",
... | Pi.zero_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Finsupp.Basic | {
"line": 471,
"column": 6
} | {
"line": 471,
"column": 14
} | [
{
"pp": "case neg\nα : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝ : AddCommMonoid M\nS : Set α\nf : α → β\nhf : Set.InjOn f S\nv₁ : α →₀ M\nhv₁ : v₁ ∈ {w | ↑w.support ⊆ S}\nv₂ : α →₀ M\nhv₂ : v₂ ∈ {w | ↑w.support ⊆ S}\neq : mapDomain f v₁ = mapDomain f v₂\na : α\nh : a ∉ v₁.support ∪ v₂.support\n⊢ v₁ a = v₂ a"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finsupp.Basic | {
"line": 471,
"column": 6
} | {
"line": 471,
"column": 14
} | [
{
"pp": "case neg\nα : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝ : AddCommMonoid M\nS : Set α\nf : α → β\nhf : Set.InjOn f S\nv₁ : α →₀ M\nhv₁ : v₁ ∈ {w | ↑w.support ⊆ S}\nv₂ : α →₀ M\nhv₂ : v₂ ∈ {w | ↑w.support ⊆ S}\neq : mapDomain f v₁ = mapDomain f v₂\na : α\nh : a ∉ v₁.support ∪ v₂.support\n⊢ v₁ a = v₂ a"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finsupp.Basic | {
"line": 471,
"column": 6
} | {
"line": 471,
"column": 14
} | [
{
"pp": "case neg\nα : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝ : AddCommMonoid M\nS : Set α\nf : α → β\nhf : Set.InjOn f S\nv₁ : α →₀ M\nhv₁ : v₁ ∈ {w | ↑w.support ⊆ S}\nv₂ : α →₀ M\nhv₂ : v₂ ∈ {w | ↑w.support ⊆ S}\neq : mapDomain f v₁ = mapDomain f v₂\na : α\nh : a ∉ v₁.support ∪ v₂.support\n⊢ v₁ a = v₂ a"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.Basic | {
"line": 649,
"column": 90
} | {
"line": 649,
"column": 98
} | [
{
"pp": "case h.h₂.h.e'_6\nα : Type u_1\nM : Type u_5\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nf : α →₀ M\na a✝¹ : α\na✝ : a = a✝¹\n⊢ a✝¹ = a",
"usedConstants": [
"congrArg",
"True",
"eq_self",
"of_eq_true",
"Eq",
"Eq.trans"
]
}
] | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finsupp.Basic | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 10
} | [
{
"pp": "α : Type u_1\nM : Type u_5\ninst✝ : Zero M\nx : α\nf : α →₀ M\nh : x ∈ f.support\n⊢ f x ∈ f.frange",
"usedConstants": [
"Finsupp.instFunLike",
"False",
"eq_false",
"congrArg",
"and_self",
"Finset",
"Finsupp.mem_support_iff._simp_1",
"Finsupp.support",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finsupp.Basic | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 10
} | [
{
"pp": "α : Type u_1\nM : Type u_5\ninst✝ : Zero M\nx : α\nf : α →₀ M\nh : x ∈ f.support\n⊢ f x ∈ f.frange",
"usedConstants": [
"Finsupp.instFunLike",
"False",
"eq_false",
"congrArg",
"and_self",
"Finset",
"Finsupp.mem_support_iff._simp_1",
"Finsupp.support",... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finsupp.Basic | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 10
} | [
{
"pp": "α : Type u_1\nM : Type u_5\ninst✝ : Zero M\nx : α\nf : α →₀ M\nh : x ∈ f.support\n⊢ f x ∈ f.frange",
"usedConstants": [
"Finsupp.instFunLike",
"False",
"eq_false",
"congrArg",
"and_self",
"Finset",
"Finsupp.mem_support_iff._simp_1",
"Finsupp.support",... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.Basic | {
"line": 740,
"column": 83
} | {
"line": 741,
"column": 10
} | [
{
"pp": "α : Type u_1\nM : Type u_5\ninst✝ : Zero M\nx : α\nf : α →₀ M\nh : x ∈ f.support\n⊢ f x ∈ f.frange",
"usedConstants": [
"Finsupp.instFunLike",
"False",
"eq_false",
"congrArg",
"and_self",
"Finset",
"Finsupp.mem_support_iff._simp_1",
"Finsupp.support",... | by
simp_all | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Finsupp.Basic | {
"line": 767,
"column": 28
} | {
"line": 767,
"column": 100
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nM : Type u_5\nN : Type u_6\nP : Type u_7\nG : Type u_8\nH : Type u_9\nR : Type u_10\nS : Type u_11\ninst✝ : Zero M\np✝ p : α → Prop\nf : α →₀ M\na : Subtype p\n⊢ a ∈ Finset.subtype p f.support ↔ (⇑f ∘ Subtype.val) a ≠ 0",
"usedConstants": [
... | simp only [@mem_subtype _ _ (Classical.decPred p), mem_support_iff]; rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finsupp.Basic | {
"line": 767,
"column": 28
} | {
"line": 767,
"column": 100
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nM : Type u_5\nN : Type u_6\nP : Type u_7\nG : Type u_8\nH : Type u_9\nR : Type u_10\nS : Type u_11\ninst✝ : Zero M\np✝ p : α → Prop\nf : α →₀ M\na : Subtype p\n⊢ a ∈ Finset.subtype p f.support ↔ (⇑f ∘ Subtype.val) a ≠ 0",
"usedConstants": [
... | simp only [@mem_subtype _ _ (Classical.decPred p), mem_support_iff]; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.Basic | {
"line": 1000,
"column": 2
} | {
"line": 1001,
"column": 51
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝¹ : Zero M\nf : α × β →₀ M\np : α → Prop\ninst✝ : DecidablePred p\n⊢ (filter (fun a ↦ p a.1) f).curry = filter p f.curry",
"usedConstants": [
"Finsupp.instFunLike",
"Finsupp.ext",
"outParam",
"congrArg",
"Decidable",
... | ext a b
simp [filter_apply, apply_ite (DFunLike.coe · b)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finsupp.Basic | {
"line": 1000,
"column": 2
} | {
"line": 1001,
"column": 51
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝¹ : Zero M\nf : α × β →₀ M\np : α → Prop\ninst✝ : DecidablePred p\n⊢ (filter (fun a ↦ p a.1) f).curry = filter p f.curry",
"usedConstants": [
"Finsupp.instFunLike",
"Finsupp.ext",
"outParam",
"congrArg",
"Decidable",
... | ext a b
simp [filter_apply, apply_ite (DFunLike.coe · b)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.Basic | {
"line": 1189,
"column": 4
} | {
"line": 1189,
"column": 35
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nM✝ : Type u_5\nN : Type u_6\nP✝ : Type u_7\nG : Type u_8\nH : Type u_9\nR : Type u_10\nS : Type u_11\nM : Type u_12\ninst✝¹ : Zero M\nP : α → Prop\ninst✝ : DecidablePred P\nf : Subtype P →₀ M\ng : { a // ¬P a } →₀ M\na : α\n⊢ a ∈ (map (Embedding.s... | by_cases ha : P a <;> simp [ha] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Finsupp.Basic | {
"line": 1189,
"column": 4
} | {
"line": 1189,
"column": 35
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nM✝ : Type u_5\nN : Type u_6\nP✝ : Type u_7\nG : Type u_8\nH : Type u_9\nR : Type u_10\nS : Type u_11\nM : Type u_12\ninst✝¹ : Zero M\nP : α → Prop\ninst✝ : DecidablePred P\nf : Subtype P →₀ M\ng : { a // ¬P a } →₀ M\na : α\n⊢ a ∈ (map (Embedding.s... | by_cases ha : P a <;> simp [ha] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finsupp.Basic | {
"line": 1189,
"column": 4
} | {
"line": 1189,
"column": 35
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nM✝ : Type u_5\nN : Type u_6\nP✝ : Type u_7\nG : Type u_8\nH : Type u_9\nR : Type u_10\nS : Type u_11\nM : Type u_12\ninst✝¹ : Zero M\nP : α → Prop\ninst✝ : DecidablePred P\nf : Subtype P →₀ M\ng : { a // ¬P a } →₀ M\na : α\n⊢ a ∈ (map (Embedding.s... | by_cases ha : P a <;> simp [ha] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.SMul | {
"line": 139,
"column": 25
} | {
"line": 139,
"column": 54
} | [
{
"pp": "α : Type u_1\nM : Type u_3\nR : Type u_6\ninst✝⁴ : Semiring R\ninst✝³ : IsDomain R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Module.IsTorsionFree R M\nb : R\nhb : b ≠ 0\ng : α →₀ M\na : α\n⊢ a ∈ (b • g).support ↔ a ∈ g.support",
"usedConstants": [
"Finsupp.instFunLike",
"F... | simp [Finsupp.smul_apply, hb] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Finsupp.SMul | {
"line": 139,
"column": 25
} | {
"line": 139,
"column": 54
} | [
{
"pp": "α : Type u_1\nM : Type u_3\nR : Type u_6\ninst✝⁴ : Semiring R\ninst✝³ : IsDomain R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Module.IsTorsionFree R M\nb : R\nhb : b ≠ 0\ng : α →₀ M\na : α\n⊢ a ∈ (b • g).support ↔ a ∈ g.support",
"usedConstants": [
"Finsupp.instFunLike",
"F... | simp [Finsupp.smul_apply, hb] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finsupp.SMul | {
"line": 139,
"column": 25
} | {
"line": 139,
"column": 54
} | [
{
"pp": "α : Type u_1\nM : Type u_3\nR : Type u_6\ninst✝⁴ : Semiring R\ninst✝³ : IsDomain R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Module.IsTorsionFree R M\nb : R\nhb : b ≠ 0\ng : α →₀ M\na : α\n⊢ a ∈ (b • g).support ↔ a ∈ g.support",
"usedConstants": [
"Finsupp.instFunLike",
"F... | simp [Finsupp.smul_apply, hb] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.BigOperators.Ring.Finset | {
"line": 115,
"column": 28
} | {
"line": 115,
"column": 36
} | [
{
"pp": "case h₁.bc.h1\nι : Type u_1\nR : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : PartialOrder R\ninst✝ : CanonicallyOrderedAdd R\nf g h : ι → R\ns : Finset ι\ni : ι\nhi : i ∈ s\nh2i : g i + h i ≤ f i\nhgf : ∀ j ∈ s, j ≠ i → g j ≤ f j\nhhf : ∀ j ∈ s, j ≠ i → h j ≤ f j\nj : ι\nhj : j ∈ s \\ {i}\n⊢ g j ≤ f j"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.BigOperators.Ring.Finset | {
"line": 115,
"column": 28
} | {
"line": 115,
"column": 36
} | [
{
"pp": "case h₂.bc.h1\nι : Type u_1\nR : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : PartialOrder R\ninst✝ : CanonicallyOrderedAdd R\nf g h : ι → R\ns : Finset ι\ni : ι\nhi : i ∈ s\nh2i : g i + h i ≤ f i\nhgf : ∀ j ∈ s, j ≠ i → g j ≤ f j\nhhf : ∀ j ∈ s, j ≠ i → h j ≤ f j\nj : ι\nhj : j ∈ s \\ {i}\n⊢ h j ≤ f j"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Interval.Set.Fin | {
"line": 62,
"column": 2
} | {
"line": 63,
"column": 18
} | [
{
"pp": "n : ℕ\ni : Fin n\n⊢ val '' Iic i = Iic ↑i",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Fin.is_lt._simp_1",
"id",
"Fin.preimage_val_Iic_val",
"HasSubset.Subset",
"Fin.val",
"Fin.instPartialOrder",
... | rw [← preimage_val_Iic_val, image_preimage_eq_of_subset]
simp [range_val] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Fin | {
"line": 62,
"column": 2
} | {
"line": 63,
"column": 18
} | [
{
"pp": "n : ℕ\ni : Fin n\n⊢ val '' Iic i = Iic ↑i",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Fin.is_lt._simp_1",
"id",
"Fin.preimage_val_Iic_val",
"HasSubset.Subset",
"Fin.val",
"Fin.instPartialOrder",
... | rw [← preimage_val_Iic_val, image_preimage_eq_of_subset]
simp [range_val] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Fin | {
"line": 806,
"column": 71
} | {
"line": 806,
"column": 93
} | [
{
"pp": "n : ℕ\ni : Fin n\n⊢ rev ⁻¹' Iio i = Ioi i.rev",
"usedConstants": [
"Set.ext",
"Set.Ioi",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Membership.mem",
"Set.mem_Ioi._simp_1",
"Set.mem_preimage._simp_1",
"iff_self",
"Iff",
... | ext; simp [rev_lt_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Fin | {
"line": 806,
"column": 71
} | {
"line": 806,
"column": 93
} | [
{
"pp": "n : ℕ\ni : Fin n\n⊢ rev ⁻¹' Iio i = Ioi i.rev",
"usedConstants": [
"Set.ext",
"Set.Ioi",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Membership.mem",
"Set.mem_Ioi._simp_1",
"Set.mem_preimage._simp_1",
"iff_self",
"Iff",
... | ext; simp [rev_lt_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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