module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 365
values | kind stringclasses 368
values |
|---|---|---|---|---|---|---|
Mathlib.Algebra.GroupWithZero.Units.Basic | {
"line": 47,
"column": 12
} | {
"line": 47,
"column": 56
} | [
{
"pp": "M₀ : Type u_2\ninst✝ : MonoidWithZero M₀\nu : M₀ˣ\na : M₀\nh : ↑u * a = 0\n⊢ a = 0",
"usedConstants": [
"Units.val",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"mul_eq_zero_of_right",
"Units",
"Eq.mp",
"Inv.inv",
"MonoidWithZero.toMulZeroOne... | by simpa using mul_eq_zero_of_right (↑u⁻¹) h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.GroupWithZero.Units.Basic | {
"line": 204,
"column": 59
} | {
"line": 206,
"column": 5
} | [
{
"pp": "G₀ : Type u_3\ninst✝ : GroupWithZero G₀\nh : 1 ≠ 0\n⊢ mk0 1 h = 1",
"usedConstants": [
"Units.val",
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"DivisionMonoid.toDivInvOneMonoid",
... | by
ext
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Ring.InjSurj | {
"line": 101,
"column": 59
} | {
"line": 101,
"column": 75
} | [
{
"pp": "R : Type u_1\nS✝ : Type u_2\nf✝ : S✝ → R\nhf✝ : Injective f✝\ninst✝²⁰ : Add S✝\ninst✝¹⁹ : Mul S✝\ninst✝¹⁸ : Zero S✝\ninst✝¹⁷ : One S✝\ninst✝¹⁶ : Neg S✝\ninst✝¹⁵ : Sub S✝\ninst✝¹⁴ : SMul ℕ S✝\ninst✝¹³ : SMul ℤ S✝\ninst✝¹² : Pow S✝ ℕ\ninst✝¹¹ : NatCast S✝\ninst✝¹⁰ : IntCast S✝\nS : Type ?u.5267\ninst✝⁹ :... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Int.Cast.Lemmas | {
"line": 60,
"column": 28
} | {
"line": 60,
"column": 44
} | [
{
"pp": "case ofNat\nα : Type u_3\ninst✝¹ : AddGroupWithOne α\ninst✝ : CharZero α\na✝ : ℕ\nh : ↑↑a✝ = 0\n⊢ ofNat a✝ = 0",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Int.cast_natCast",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddGroupWithOne.toAddMon... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Int.Cast.Lemmas | {
"line": 94,
"column": 21
} | {
"line": 94,
"column": 49
} | [
{
"pp": "α : Type u_3\ninst✝ : NonAssocRing α\nn : ℕ\nx : α\n⊢ Commute (↑↑n) x",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"Commute",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring"... | simpa using n.cast_commute x | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Data.Int.Cast.Lemmas | {
"line": 94,
"column": 21
} | {
"line": 94,
"column": 49
} | [
{
"pp": "α : Type u_3\ninst✝ : NonAssocRing α\nn : ℕ\nx : α\n⊢ Commute (↑↑n) x",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"Commute",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring"... | simpa using n.cast_commute x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Int.Cast.Lemmas | {
"line": 94,
"column": 21
} | {
"line": 94,
"column": 49
} | [
{
"pp": "α : Type u_3\ninst✝ : NonAssocRing α\nn : ℕ\nx : α\n⊢ Commute (↑↑n) x",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"Commute",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring"... | simpa using n.cast_commute x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.Cast.Lemmas | {
"line": 104,
"column": 51
} | {
"line": 104,
"column": 67
} | [
{
"pp": "α : Type u_3\ninst✝ : NonAssocRing α\na : α\nn : ℕ\n⊢ ↑n * a = ↑↑n * a",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Int.cast_natCast",
"HMul.hMul",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Monoid.Defs | {
"line": 30,
"column": 33
} | {
"line": 30,
"column": 62
} | [
{
"pp": "α✝ : Type u_1\nα : Type u_2\ninst✝¹ : AddCommMonoid α\ninst✝ : Preorder α\nadd_le_add_left : ∀ (a b : α), a ≤ b → ∀ (c : α), a + c ≤ b + c\na b : α\nh : a ≤ b\nc : α\n⊢ a + c ≤ b + c",
"usedConstants": []
}
] | exact add_le_add_left a b h c | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Group.Defs | {
"line": 121,
"column": 45
} | {
"line": 121,
"column": 82
} | [
{
"pp": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedMonoid α\na : α\n⊢ a < a⁻¹ ↔ a < 1",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"InvOneClass.toOne",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
"DivisionCommMonoid.toDivisionMonoid",
... | by contrapose!; exact inv_le_self_iff | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Monoid.Unbundled.Basic | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 52
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝² : Mul α\ninst✝¹ : PartialOrder α\ninst✝ : MulLeftStrictMono α\na b c : α\nh' : ¬c = b\nh : b ≤ c\n⊢ ¬a * c = a * b",
"usedConstants": [
"Preorder.toLT",
"HMul.hMul",
"PartialOrder.toPreorder",
"mul_lt_mul_right",
"LT.lt.ne'",
"LE.le... | exact mul_lt_mul_right (h.lt_of_ne' h') a |>.ne' | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Monoid.Unbundled.Basic | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 52
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝² : Mul α\ninst✝¹ : PartialOrder α\ninst✝ : MulLeftStrictMono α\na b c : α\nh' : ¬c = b\nh : b ≤ c\n⊢ ¬a * c = a * b",
"usedConstants": [
"Preorder.toLT",
"HMul.hMul",
"PartialOrder.toPreorder",
"mul_lt_mul_right",
"LT.lt.ne'",
"LE.le... | exact mul_lt_mul_right (h.lt_of_ne' h') a |>.ne' | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.Unbundled.Basic | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 52
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝² : Mul α\ninst✝¹ : PartialOrder α\ninst✝ : MulLeftStrictMono α\na b c : α\nh' : ¬c = b\nh : b ≤ c\n⊢ ¬a * c = a * b",
"usedConstants": [
"Preorder.toLT",
"HMul.hMul",
"PartialOrder.toPreorder",
"mul_lt_mul_right",
"LT.lt.ne'",
"LE.le... | exact mul_lt_mul_right (h.lt_of_ne' h') a |>.ne' | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 360,
"column": 6
} | {
"line": 360,
"column": 30
} | [
{
"pp": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LE α\ninst✝ : MulLeftMono α\na b c : α\n⊢ a * b⁻¹ ≤ c ↔ a ≤ b * c",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
... | ← inv_mul_le_iff_le_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.Lattice | {
"line": 127,
"column": 68
} | {
"line": 127,
"column": 92
} | [
{
"pp": "α✝ : Type u_1\ninst✝⁴ : Lattice α✝\ninst✝³ : CommGroup α✝\nα : Type u_2\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : MulLeftMono α\nx y z : α\n⊢ (x ⊓ (y ⊓ z)) * ((x ⊔ y) ⊓ (x ⊔ z)) ≤ x * (y ⊓ z)",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"D... | ← inv_mul_le_iff_le_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.RelIso.Basic | {
"line": 604,
"column": 78
} | {
"line": 604,
"column": 98
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nu : δ → δ → Prop\nf : r ≃r s\na b : β\n⊢ s a (f (f.symm b)) ↔ s a b",
"usedConstants": [
"Eq.mpr",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
... | f.1.apply_symm_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 110,
"column": 2
} | {
"line": 112,
"column": 20
} | [
{
"pp": "α : Type u_1\ninst✝³ : Lattice α\ninst✝² : Group α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\na : α\n⊢ 1 ≤ |a|ₘ",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"inv_mul_cancel",
"InvOneClass.toOne",
"HM... | apply pow_two_semiclosed _
rw [mabs, pow_two, mul_sup, sup_mul, ← pow_two, inv_mul_cancel, sup_comm, ← sup_assoc]
apply le_sup_right | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 110,
"column": 2
} | {
"line": 112,
"column": 20
} | [
{
"pp": "α : Type u_1\ninst✝³ : Lattice α\ninst✝² : Group α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\na : α\n⊢ 1 ≤ |a|ₘ",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"inv_mul_cancel",
"InvOneClass.toOne",
"HM... | apply pow_two_semiclosed _
rw [mabs, pow_two, mul_sup, sup_mul, ← pow_two, inv_mul_cancel, sup_comm, ← sup_assoc]
apply le_sup_right | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Hom.Basic | {
"line": 344,
"column": 48
} | {
"line": 346,
"column": 5
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α →o β\n⊢ f.comp id = f",
"usedConstants": [
"OrderHom.id",
"OrderHom.comp",
"funext",
"OrderHom.ext",
"OrderHom.instFunLike",
"Eq.refl",
"DFunLike.coe",
"OrderHom"
]
}
] | by
ext
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Hom.Basic | {
"line": 349,
"column": 48
} | {
"line": 351,
"column": 5
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α →o β\n⊢ id.comp f = f",
"usedConstants": [
"OrderHom.id",
"OrderHom.comp",
"funext",
"OrderHom.ext",
"OrderHom.instFunLike",
"Eq.refl",
"DFunLike.coe",
"OrderHom"
]
}
] | by
ext
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Hom.Basic | {
"line": 1169,
"column": 6
} | {
"line": 1169,
"column": 28
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝³ : SemilatticeSup α\ninst✝² : OrderTop α\ninst✝¹ : SemilatticeSup β\ninst✝ : OrderTop β\na b : α\nf : α ≃o β\nha : Codisjoint a b\n⊢ Codisjoint (f a) (f b)",
"usedConstants": [
"Eq.mpr",
"Codisjoint",
"congrArg",
"PartialOrder.toPreorder",
... | codisjoint_iff_le_sup, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 78
} | [
{
"pp": "α : Type u_1\ninst✝³ : Mul α\ninst✝² : Zero α\ninst✝¹ : Preorder α\ninst✝ : Std.Commutative fun x1 x2 ↦ x1 * x2\n⊢ PosMulStrictMono α ↔ MulPosStrictMono α",
"usedConstants": [
"Preorder.toLT",
"_private.Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs.0.posMulStrictMono_iff_mulPosStri... | simp only [posMulStrictMono_iff, mulPosStrictMono_iff, Std.Commutative.comm] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 78
} | [
{
"pp": "α : Type u_1\ninst✝³ : Mul α\ninst✝² : Zero α\ninst✝¹ : Preorder α\ninst✝ : Std.Commutative fun x1 x2 ↦ x1 * x2\n⊢ PosMulStrictMono α ↔ MulPosStrictMono α",
"usedConstants": [
"Preorder.toLT",
"_private.Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs.0.posMulStrictMono_iff_mulPosStri... | simp only [posMulStrictMono_iff, mulPosStrictMono_iff, Std.Commutative.comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 78
} | [
{
"pp": "α : Type u_1\ninst✝³ : Mul α\ninst✝² : Zero α\ninst✝¹ : Preorder α\ninst✝ : Std.Commutative fun x1 x2 ↦ x1 * x2\n⊢ PosMulStrictMono α ↔ MulPosStrictMono α",
"usedConstants": [
"Preorder.toLT",
"_private.Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs.0.posMulStrictMono_iff_mulPosStri... | simp only [posMulStrictMono_iff, mulPosStrictMono_iff, Std.Commutative.comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.GCD | {
"line": 203,
"column": 15
} | {
"line": 203,
"column": 24
} | [
{
"pp": "x y : ℤ\nhc : x = 0 ∧ y = 0\n⊢ gcd 0 y = 0",
"usedConstants": [
"Int.gcd",
"Eq.mpr",
"congrArg",
"id",
"instOfNatNat",
"Int",
"And.right",
"instOfNat",
"Nat",
"OfNat.ofNat",
"Eq"
]
}
] | hc.right, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.Int | {
"line": 51,
"column": 24
} | {
"line": 51,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ℤ\n⊢ ↑n.natAbs = ↑↑n.natAbs",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
"AddMonoidWithOne.toNatCast",
"Int",
"AddGroupWithOne... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 812,
"column": 2
} | {
"line": 812,
"column": 60
} | [
{
"pp": "R : Type u\ninst✝⁵ : Ring R\ninst✝⁴ : LinearOrder R\na b : R\ninst✝³ : PosMulStrictMono R\ninst✝² : MulPosStrictMono R\ninst✝¹ : AddLeftMono R\ninst✝ : AddLeftReflectLE R\n⊢ 0 ≤ a * b ↔ (a < 0 → b ≤ 0) ∧ (b < 0 → a ≤ 0)",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"HMul.hMul",
... | rw [← neg_mul_neg, mul_nonneg_iff_pos_imp_nonneg (R := R)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 104,
"column": 59
} | {
"line": 104,
"column": 99
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithTop α\n⊢ x + y = ⊤ ↔ x = ⊤ ∨ y = ⊤",
"usedConstants": [
"False",
"congrArg",
"WithTop.coe_ne_top._simp_1",
"WithTop.add_top",
"WithTop.some",
"iff_self",
"instHAdd",
"Iff",
"WithTop.top",
"HAdd.hAdd",
... | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 104,
"column": 59
} | {
"line": 104,
"column": 99
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithTop α\n⊢ x + y = ⊤ ↔ x = ⊤ ∨ y = ⊤",
"usedConstants": [
"False",
"congrArg",
"WithTop.coe_ne_top._simp_1",
"WithTop.add_top",
"WithTop.some",
"iff_self",
"instHAdd",
"Iff",
"WithTop.top",
"HAdd.hAdd",
... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 104,
"column": 59
} | {
"line": 104,
"column": 99
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithTop α\n⊢ x + y = ⊤ ↔ x = ⊤ ∨ y = ⊤",
"usedConstants": [
"False",
"congrArg",
"WithTop.coe_ne_top._simp_1",
"WithTop.add_top",
"WithTop.some",
"iff_self",
"instHAdd",
"Iff",
"WithTop.top",
"HAdd.hAdd",
... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 106,
"column": 51
} | {
"line": 106,
"column": 91
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithTop α\n⊢ x + y ≠ ⊤ ↔ x ≠ ⊤ ∧ y ≠ ⊤",
"usedConstants": [
"False",
"and_true",
"congrArg",
"and_self",
"WithTop.coe_ne_top._simp_1",
"not_true_eq_false",
"Ne",
"WithTop.add_top",
"WithTop.some",
"iff_self... | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 106,
"column": 51
} | {
"line": 106,
"column": 91
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithTop α\n⊢ x + y ≠ ⊤ ↔ x ≠ ⊤ ∧ y ≠ ⊤",
"usedConstants": [
"False",
"and_true",
"congrArg",
"and_self",
"WithTop.coe_ne_top._simp_1",
"not_true_eq_false",
"Ne",
"WithTop.add_top",
"WithTop.some",
"iff_self... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 106,
"column": 51
} | {
"line": 106,
"column": 91
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithTop α\n⊢ x + y ≠ ⊤ ↔ x ≠ ⊤ ∧ y ≠ ⊤",
"usedConstants": [
"False",
"and_true",
"congrArg",
"and_self",
"WithTop.coe_ne_top._simp_1",
"not_true_eq_false",
"Ne",
"WithTop.add_top",
"WithTop.some",
"iff_self... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 171,
"column": 24
} | {
"line": 171,
"column": 64
} | [
{
"pp": "α : Type u\ninst✝² : Add α\nx y : WithTop α\ninst✝¹ : LE α\ninst✝ : AddRightReflectLE α\nz : α\n⊢ x + ↑z ≤ y + ↑z → x ≤ y",
"usedConstants": [
"Eq.refl",
"WithTop"
]
}
] | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 179,
"column": 24
} | {
"line": 179,
"column": 64
} | [
{
"pp": "α : Type u\ninst✝² : Add α\nx y : WithTop α\ninst✝¹ : LT α\ninst✝ : AddRightStrictMono α\nz : α\n⊢ x < y → x + ↑z < y + ↑z",
"usedConstants": [
"Eq.refl",
"WithTop"
]
}
] | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 222,
"column": 8
} | {
"line": 222,
"column": 91
} | [
{
"pp": "α : Type u\ninst✝³ : Add α\nx : WithTop α\ninst✝² : Nonempty α\ninst✝¹ : Preorder α\ninst✝ : AddLeftReflectLE α\n⊢ AddLECancellable x → x ≠ ⊤",
"usedConstants": [
"False",
"Preorder.toLT",
"WithTop.coe_lt_top",
"instReflLe",
"WithTop.instPreorder",
"congrArg",
... | by rintro h rfl; exact (coe_lt_top <| Classical.arbitrary _).not_ge <| h <| by simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 462,
"column": 59
} | {
"line": 462,
"column": 99
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithBot α\n⊢ x + y = ⊥ ↔ x = ⊥ ∨ y = ⊥",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"congrArg",
"WithBot.coe_ne_bot._simp_3",
"WithBot.add_bot",
"Bot.bot",
"iff_self",
"instHAdd",
"Iff",
"... | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 462,
"column": 59
} | {
"line": 462,
"column": 99
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithBot α\n⊢ x + y = ⊥ ↔ x = ⊥ ∨ y = ⊥",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"congrArg",
"WithBot.coe_ne_bot._simp_3",
"WithBot.add_bot",
"Bot.bot",
"iff_self",
"instHAdd",
"Iff",
"... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 462,
"column": 59
} | {
"line": 462,
"column": 99
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithBot α\n⊢ x + y = ⊥ ↔ x = ⊥ ∨ y = ⊥",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"congrArg",
"WithBot.coe_ne_bot._simp_3",
"WithBot.add_bot",
"Bot.bot",
"iff_self",
"instHAdd",
"Iff",
"... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 464,
"column": 51
} | {
"line": 464,
"column": 91
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithBot α\n⊢ x + y ≠ ⊥ ↔ x ≠ ⊥ ∧ y ≠ ⊥",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"and_true",
"congrArg",
"and_self",
"WithBot.coe_ne_bot._simp_3",
"WithBot.add_bot",
"not_true_eq_false",
"Ne"... | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 464,
"column": 51
} | {
"line": 464,
"column": 91
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithBot α\n⊢ x + y ≠ ⊥ ↔ x ≠ ⊥ ∧ y ≠ ⊥",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"and_true",
"congrArg",
"and_self",
"WithBot.coe_ne_bot._simp_3",
"WithBot.add_bot",
"not_true_eq_false",
"Ne"... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 464,
"column": 51
} | {
"line": 464,
"column": 91
} | [
{
"pp": "α : Type u\ninst✝ : Add α\nx y : WithBot α\n⊢ x + y ≠ ⊥ ↔ x ≠ ⊥ ∧ y ≠ ⊥",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"and_true",
"congrArg",
"and_self",
"WithBot.coe_ne_bot._simp_3",
"WithBot.add_bot",
"not_true_eq_false",
"Ne"... | cases x <;> cases y <;> simp [← coe_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 496,
"column": 24
} | {
"line": 496,
"column": 64
} | [
{
"pp": "α : Type u\ninst✝¹ : Add α\nx y : WithBot α\ninst✝ : IsRightCancelAdd α\nz : α\n⊢ x + ↑z = y + ↑z ↔ x = y",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"congrArg",
"WithBot.coe_ne_bot._simp_3",
"Bot.bot",
"iff_self",
"instHAdd",
"Iff"... | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Sub.Basic | {
"line": 175,
"column": 28
} | {
"line": 175,
"column": 68
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : LinearOrder α\ninst✝³ : CanonicallyOrderedAdd α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\ninst✝ : AddLeftReflectLE α\na b : α\n⊢ a - (a - min a b) = min a b",
"usedConstants": [
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"congrArg",
... | tsub_tsub_cancel_of_le (min_le_left a _) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Sub.Basic | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 55
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝⁴ : AddCommMonoid α\ninst✝³ : LinearOrder α\ninst✝² : CanonicallyOrderedAdd α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b : α\nh : a ≤ b\n⊢ a - b + b = max a b",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"tsub_eq_zero_of_le",
"congr... | rw [max_eq_right h, tsub_eq_zero_of_le h, zero_add] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Sub.Basic | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 55
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝⁴ : AddCommMonoid α\ninst✝³ : LinearOrder α\ninst✝² : CanonicallyOrderedAdd α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b : α\nh : a ≤ b\n⊢ a - b + b = max a b",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"tsub_eq_zero_of_le",
"congr... | rw [max_eq_right h, tsub_eq_zero_of_le h, zero_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Sub.Basic | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 55
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝⁴ : AddCommMonoid α\ninst✝³ : LinearOrder α\ninst✝² : CanonicallyOrderedAdd α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b : α\nh : a ≤ b\n⊢ a - b + b = max a b",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"tsub_eq_zero_of_le",
"congr... | rw [max_eq_right h, tsub_eq_zero_of_le h, zero_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 529,
"column": 24
} | {
"line": 529,
"column": 64
} | [
{
"pp": "α : Type u\ninst✝² : Add α\nx y : WithBot α\ninst✝¹ : LE α\ninst✝ : AddRightReflectLE α\nz : α\n⊢ x + ↑z ≤ y + ↑z → x ≤ y",
"usedConstants": [
"WithBot",
"Eq.refl"
]
}
] | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 537,
"column": 24
} | {
"line": 537,
"column": 64
} | [
{
"pp": "α : Type u\ninst✝² : Add α\nx y : WithBot α\ninst✝¹ : LT α\ninst✝ : AddRightStrictMono α\nz : α\n⊢ x < y → x + ↑z < y + ↑z",
"usedConstants": [
"WithBot",
"Eq.refl"
]
}
] | cases x <;> cases y <;> simp [← coe_add] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Nat.Find | {
"line": 208,
"column": 2
} | {
"line": 208,
"column": 28
} | [
{
"pp": "k : ℕ\nP : ℕ → Prop\ninst✝ : DecidablePred P\n⊢ findGreatest P k = 0 ↔ ∀ ⦃n : ℕ⦄, 0 < n → n ≤ k → ¬P n",
"usedConstants": [
"False",
"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_zero_iff._simp_1_1",
"congrArg",
"not_true_eq_false",
"Ne",
"instOfNatNat",
... | simp [findGreatest_eq_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Nat.Find | {
"line": 208,
"column": 2
} | {
"line": 208,
"column": 28
} | [
{
"pp": "k : ℕ\nP : ℕ → Prop\ninst✝ : DecidablePred P\n⊢ findGreatest P k = 0 ↔ ∀ ⦃n : ℕ⦄, 0 < n → n ≤ k → ¬P n",
"usedConstants": [
"False",
"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_zero_iff._simp_1_1",
"congrArg",
"not_true_eq_false",
"Ne",
"instOfNatNat",
... | simp [findGreatest_eq_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Find | {
"line": 208,
"column": 2
} | {
"line": 208,
"column": 28
} | [
{
"pp": "k : ℕ\nP : ℕ → Prop\ninst✝ : DecidablePred P\n⊢ findGreatest P k = 0 ↔ ∀ ⦃n : ℕ⦄, 0 < n → n ≤ k → ¬P n",
"usedConstants": [
"False",
"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_zero_iff._simp_1_1",
"congrArg",
"not_true_eq_false",
"Ne",
"instOfNatNat",
... | simp [findGreatest_eq_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 323,
"column": 6
} | {
"line": 323,
"column": 20
} | [
{
"pp": "case coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝³ : Preorder α\ninst✝² : Preorder β\nx y : WithZero α\na b : α\ninst✝¹ : Mul α\ninst✝ : MulLeftMono α\na✝¹ a✝ c : α\nhbc' : a✝ ≤ c\nhbc : ↑a✝ ≤ ↑c\n⊢ ↑a✝¹ * ↑a✝ ≤ ↑a✝¹ * ↑c",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toM... | ← coe_mul _ c, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 355,
"column": 30
} | {
"line": 355,
"column": 65
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : MulOneClass α\ninst✝ : MulOneClass β\nf : α →* β\nhf : StrictMono ⇑f\n⊢ StrictMono ⇑(map' f)",
"usedConstants": [
"Eq.mpr",
"False",
"Preorder.toLT",
"MonoidHom.instFunLike",
"_private.Mathl... | simpa [StrictMono, WithZero.forall] | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 355,
"column": 30
} | {
"line": 355,
"column": 65
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : MulOneClass α\ninst✝ : MulOneClass β\nf : α →* β\nhf : StrictMono ⇑f\n⊢ StrictMono ⇑(map' f)",
"usedConstants": [
"Eq.mpr",
"False",
"Preorder.toLT",
"MonoidHom.instFunLike",
"_private.Mathl... | simpa [StrictMono, WithZero.forall] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 355,
"column": 30
} | {
"line": 355,
"column": 65
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : MulOneClass α\ninst✝ : MulOneClass β\nf : α →* β\nhf : StrictMono ⇑f\n⊢ StrictMono ⇑(map' f)",
"usedConstants": [
"Eq.mpr",
"False",
"Preorder.toLT",
"MonoidHom.instFunLike",
"_private.Mathl... | simpa [StrictMono, WithZero.forall] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 370,
"column": 36
} | {
"line": 370,
"column": 47
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na : WithZero (Multiplicative α)\nb : α\nha : a ≠ 0\nh : unzero ha < ofAdd b\n⊢ toAdd (unzero ha) < b",
"usedConstants": [
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"Eq.mp",
"Equiv",
"WithZero.unzero",
"Multiplicat... | ← toAdd_lt, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Floor.Defs | {
"line": 211,
"column": 4
} | {
"line": 211,
"column": 9
} | [
{
"pp": "F : Type u_1\nα✝ : Type u_2\nβ : Type u_3\nα : Type ?u.13448\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nbounded : ∀ (x : α), ∃ n, x ≤ ↑n\nbelow : ∀ (x : α), ∃ n, ↑n ≤ x\nx : α\nn : ℕ\nhn : x ≤ ↑n\n⊢ ∃ n, x ≤ ↑n",
"usedConstants": [
"Int.cast",
"PartialOrder... | use n | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Order.WithBot | {
"line": 595,
"column": 4
} | {
"line": 595,
"column": 92
} | [
{
"pp": "case none\nα : Type u_1\ninst✝¹ : Preorder α\ny : WithBot α\ninst✝ : NoBotOrder α\n⊢ (∀ (a : α), ↑a ≤ none → ↑a ≤ y) ↔ none ≤ y",
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"WithBot.some",
"WithBot",
"WithBot.coe_le_coe._simp_2",
"congrArg",
"With... | simpa [WithBot.none_eq_bot, eq_bot_iff_forall_le] using fun a ha ↦ (not_isBot _ ha).elim | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.WithBot | {
"line": 595,
"column": 4
} | {
"line": 595,
"column": 92
} | [
{
"pp": "case none\nα : Type u_1\ninst✝¹ : Preorder α\ny : WithBot α\ninst✝ : NoBotOrder α\n⊢ (∀ (a : α), ↑a ≤ none → ↑a ≤ y) ↔ none ≤ y",
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"WithBot.some",
"WithBot",
"WithBot.coe_le_coe._simp_2",
"congrArg",
"With... | simpa [WithBot.none_eq_bot, eq_bot_iff_forall_le] using fun a ha ↦ (not_isBot _ ha).elim | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.WithBot | {
"line": 595,
"column": 4
} | {
"line": 595,
"column": 92
} | [
{
"pp": "case none\nα : Type u_1\ninst✝¹ : Preorder α\ny : WithBot α\ninst✝ : NoBotOrder α\n⊢ (∀ (a : α), ↑a ≤ none → ↑a ≤ y) ↔ none ≤ y",
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"WithBot.some",
"WithBot",
"WithBot.coe_le_coe._simp_2",
"congrArg",
"With... | simpa [WithBot.none_eq_bot, eq_bot_iff_forall_le] using fun a ha ↦ (not_isBot _ ha).elim | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Floor.Defs | {
"line": 315,
"column": 82
} | {
"line": 315,
"column": 98
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\na : α\nn : ℕ\nha : 0 ≤ a\n⊢ ↑↑n ≤ a ↔ ↑n ≤ a",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Int.cas... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Floor.Defs | {
"line": 316,
"column": 51
} | {
"line": 316,
"column": 67
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\na : α\nn : ℕ\n⊢ a ≤ ↑↑n ↔ a ≤ ↑n",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Int.cast_natCast",
... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 45,
"column": 28
} | {
"line": 45,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ a < ↑1 ↔ a < 1",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
... | rw [Nat.cast_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 45,
"column": 28
} | {
"line": 45,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ a < ↑1 ↔ a < 1",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
... | rw [Nat.cast_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 45,
"column": 28
} | {
"line": 45,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ a < ↑1 ↔ a < 1",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
... | rw [Nat.cast_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.NormNum.Result | {
"line": 191,
"column": 27
} | {
"line": 191,
"column": 63
} | [
{
"pp": "α : Type u_1\ninst✝ : Ring α\nn : ℕ\n⊢ ↑(Int.negOfNat n) = -↑n",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"NegZeroClass.toNeg",
"Int.cast_natCast",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddGroupWithOne.toAddM... | simp [Int.negOfNat_eq, Int.cast_neg] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Tactic.NormNum.Result | {
"line": 191,
"column": 27
} | {
"line": 191,
"column": 63
} | [
{
"pp": "α : Type u_1\ninst✝ : Ring α\nn : ℕ\n⊢ ↑(Int.negOfNat n) = -↑n",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"NegZeroClass.toNeg",
"Int.cast_natCast",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddGroupWithOne.toAddM... | simp [Int.negOfNat_eq, Int.cast_neg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.NormNum.Result | {
"line": 191,
"column": 27
} | {
"line": 191,
"column": 63
} | [
{
"pp": "α : Type u_1\ninst✝ : Ring α\nn : ℕ\n⊢ ↑(Int.negOfNat n) = -↑n",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"NegZeroClass.toNeg",
"Int.cast_natCast",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddGroupWithOne.toAddM... | simp [Int.negOfNat_eq, Int.cast_neg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Basic | {
"line": 27,
"column": 40
} | {
"line": 29,
"column": 25
} | [
{
"pp": "R : Type u_3\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\ninst✝² : ExistsAddOfLE R\ninst✝¹ : PosMulMono R\ninst✝ : AddLeftMono R\nx : R\nh : IsSquare x\n⊢ 0 ≤ x",
"usedConstants": [
"mul_self_nonneg",
"HMul.hMul",
"PartialOrder.toPreorder",
"NonUnitalNonAssocSemiring.toMulZ... | by
rcases h with ⟨y, rfl⟩
exact mul_self_nonneg y | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.NormNum.Basic | {
"line": 222,
"column": 27
} | {
"line": 236,
"column": 72
} | [
{
"pp": "α : Type u_1\ninst✝ : Ring α\nf : α → α → α\na b : α\nna nb nc : ℤ\nda db dc k : ℕ\n⊢ f = HAdd.hAdd →\n IsRat a na da →\n IsRat b nb db → (na.mul ↑db).add (nb.mul ↑da) = (↑k).mul nc → da.mul db = k.mul dc → IsRat (f a b) nc dc",
"usedConstants": [
"add_mul",
"Int.cast",
"E... | by
rintro rfl ⟨_, rfl⟩ ⟨_, rfl⟩ (h₁ : na * db + nb * da = k * nc) (h₂ : da * db = k * dc)
have : Invertible (↑(da * db) : α) := by simpa using invertibleMul (da:α) db
have := invertibleOfMul' (α := α) h₂
use this
have H := (Nat.cast_commute (α := α) da db).invOf_left.invOf_right.right_comm
have h₁ := congr_... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 431,
"column": 14
} | {
"line": 431,
"column": 63
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : ¬a ≤ b\n⊢ Icc a b = Ioc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"Set.Icc_eq_empty",
"le_of_lt",
"Preorder.toLE",
"mt",
"id",
"LE.le",
"Set.Ioc_eq_empty... | rw [Icc_eq_empty h, Ioc_eq_empty (mt le_of_lt h)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 431,
"column": 14
} | {
"line": 431,
"column": 63
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : ¬a ≤ b\n⊢ Icc a b = Ioc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"Set.Icc_eq_empty",
"le_of_lt",
"Preorder.toLE",
"mt",
"id",
"LE.le",
"Set.Ioc_eq_empty... | rw [Icc_eq_empty h, Ioc_eq_empty (mt le_of_lt h)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Basic | {
"line": 431,
"column": 14
} | {
"line": 431,
"column": 63
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : ¬a ≤ b\n⊢ Icc a b = Ioc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"Set.Icc_eq_empty",
"le_of_lt",
"Preorder.toLE",
"mt",
"id",
"LE.le",
"Set.Ioc_eq_empty... | rw [Icc_eq_empty h, Ioc_eq_empty (mt le_of_lt h)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 449,
"column": 14
} | {
"line": 449,
"column": 49
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : ¬a < b\n⊢ Ioo a b = Ioc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"congrArg",
"id",
"Set.Ioc_eq_empty",
"Set.instEmptyCollection",
"Eq.refl",
"EmptyCollection.emptyCollection",
"Set.Ioo_eq_empty... | rw [Ioo_eq_empty h, Ioc_eq_empty h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 449,
"column": 14
} | {
"line": 449,
"column": 49
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : ¬a < b\n⊢ Ioo a b = Ioc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"congrArg",
"id",
"Set.Ioc_eq_empty",
"Set.instEmptyCollection",
"Eq.refl",
"EmptyCollection.emptyCollection",
"Set.Ioo_eq_empty... | rw [Ioo_eq_empty h, Ioc_eq_empty h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Basic | {
"line": 449,
"column": 14
} | {
"line": 449,
"column": 49
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : ¬a < b\n⊢ Ioo a b = Ioc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"congrArg",
"id",
"Set.Ioc_eq_empty",
"Set.instEmptyCollection",
"Eq.refl",
"EmptyCollection.emptyCollection",
"Set.Ioo_eq_empty... | rw [Ioo_eq_empty h, Ioc_eq_empty h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 345,
"column": 6
} | {
"line": 345,
"column": 38
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nl : NF M\nr : ℤ\nhr : r ≠ 0\nx : M\nhx : x = l.eval\n⊢ x ^ r = (l ^ r).eval",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toDivInvMonoid",
"congrArg",
"DivInvMonoid.toZPow",
"id",
"Int",
"Mathlib.Tactic.FieldSimp.z... | ← zpow'_of_ne_zero_right x r hr, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 693,
"column": 2
} | {
"line": 700,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ε : α\nhε : 0 < ε\n⊢ 2 * a * b ≤ ε * a ^ 2 + ε⁻¹ * b ^ 2",
"usedConstants": [
"Iff.mpr",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Distrib.leftDistribClass",
"Eq.mp... | have h : 2 * (ε * a) * b ≤ (ε * a) ^ 2 + b ^ 2 := two_mul_le_add_sq (ε * a) b
calc 2 * a * b
_ = 2 * a * b * (ε * ε⁻¹) := by rw [mul_inv_cancel₀ hε.ne', mul_one]
_ = (2 * (ε * a) * b) * ε⁻¹ := by simp_rw [mul_assoc, mul_comm ε, mul_assoc]
_ ≤ ((ε * a) ^ 2 + b ^ 2) * ε⁻¹ := by gcongr; exact inv_nonneg.mpr hε.le
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Field.Basic | {
"line": 693,
"column": 2
} | {
"line": 700,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ε : α\nhε : 0 < ε\n⊢ 2 * a * b ≤ ε * a ^ 2 + ε⁻¹ * b ^ 2",
"usedConstants": [
"Iff.mpr",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Distrib.leftDistribClass",
"Eq.mp... | have h : 2 * (ε * a) * b ≤ (ε * a) ^ 2 + b ^ 2 := two_mul_le_add_sq (ε * a) b
calc 2 * a * b
_ = 2 * a * b * (ε * ε⁻¹) := by rw [mul_inv_cancel₀ hε.ne', mul_one]
_ = (2 * (ε * a) * b) * ε⁻¹ := by simp_rw [mul_assoc, mul_comm ε, mul_assoc]
_ ≤ ((ε * a) ^ 2 + b ^ 2) * ε⁻¹ := by gcongr; exact inv_nonneg.mpr hε.le
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Unbundled.Rat | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 45
} | [
{
"pp": "a : ℤ\nb : ℕ\nhb : b ≠ 0\n⊢ 0 < mkRat a b ↔ 0 < a",
"usedConstants": [
"_private.Mathlib.Algebra.Order.Ring.Unbundled.Rat.0.Rat.mkRat_pos_iff._proof_1_1"
]
}
] | grind [mkRat_nonneg_iff, Rat.mkRat_eq_zero] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Algebra.Order.Ring.Unbundled.Rat | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 45
} | [
{
"pp": "a : ℤ\nb : ℕ\nhb : b ≠ 0\n⊢ 0 < mkRat a b ↔ 0 < a",
"usedConstants": [
"_private.Mathlib.Algebra.Order.Ring.Unbundled.Rat.0.Rat.mkRat_pos_iff._proof_1_1"
]
}
] | grind [mkRat_nonneg_iff, Rat.mkRat_eq_zero] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.Unbundled.Rat | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 45
} | [
{
"pp": "a : ℤ\nb : ℕ\nhb : b ≠ 0\n⊢ 0 < mkRat a b ↔ 0 < a",
"usedConstants": [
"_private.Mathlib.Algebra.Order.Ring.Unbundled.Rat.0.Rat.mkRat_pos_iff._proof_1_1"
]
}
] | grind [mkRat_nonneg_iff, Rat.mkRat_eq_zero] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.NNRat.Defs | {
"line": 335,
"column": 2
} | {
"line": 335,
"column": 73
} | [
{
"pp": "q : ℚ≥0\n⊢ 0 < q.num ↔ 0 < q",
"usedConstants": [
"NNRat.coe_eq_zero._simp_1",
"Rat.instOfNat",
"Eq.mpr",
"Rat.num",
"Preorder.toLT",
"ne_iff_gt_iff_ge._simp_1",
"Rat.num_eq_zero._simp_1",
"congrArg",
"CommSemiring.toSemiring",
"Rat",
... | simpa [num, -nonpos_iff_eq_zero] using nonpos_iff_eq_zero _ |>.not.symm | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Data.NNRat.Defs | {
"line": 335,
"column": 2
} | {
"line": 335,
"column": 73
} | [
{
"pp": "q : ℚ≥0\n⊢ 0 < q.num ↔ 0 < q",
"usedConstants": [
"NNRat.coe_eq_zero._simp_1",
"Rat.instOfNat",
"Eq.mpr",
"Rat.num",
"Preorder.toLT",
"ne_iff_gt_iff_ge._simp_1",
"Rat.num_eq_zero._simp_1",
"congrArg",
"CommSemiring.toSemiring",
"Rat",
... | simpa [num, -nonpos_iff_eq_zero] using nonpos_iff_eq_zero _ |>.not.symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.NNRat.Defs | {
"line": 335,
"column": 2
} | {
"line": 335,
"column": 73
} | [
{
"pp": "q : ℚ≥0\n⊢ 0 < q.num ↔ 0 < q",
"usedConstants": [
"NNRat.coe_eq_zero._simp_1",
"Rat.instOfNat",
"Eq.mpr",
"Rat.num",
"Preorder.toLT",
"ne_iff_gt_iff_ge._simp_1",
"Rat.num_eq_zero._simp_1",
"congrArg",
"CommSemiring.toSemiring",
"Rat",
... | simpa [num, -nonpos_iff_eq_zero] using nonpos_iff_eq_zero _ |>.not.symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 633,
"column": 2
} | {
"line": 637,
"column": 23
} | [
{
"pp": "α : Type u\nl₁ l₂ : List α\n⊢ l₁ = l₂ ↔ l₁.length = l₂.length ∧ ∀ (n : ℕ) (h₁ : n < l₁.length) (h₂ : n < l₂.length), l₁.get ⟨n, h₁⟩ = l₂.get ⟨n, h₂⟩",
"usedConstants": [
"List.get",
"Fin.mk",
"List.ext_get",
"List",
"And",
"Nat",
"And.intro",
"LT.lt",... | constructor
· rintro rfl
exact ⟨rfl, fun _ _ _ ↦ rfl⟩
· intro ⟨h₁, h₂⟩
exact ext_get h₁ h₂ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Basic | {
"line": 633,
"column": 2
} | {
"line": 637,
"column": 23
} | [
{
"pp": "α : Type u\nl₁ l₂ : List α\n⊢ l₁ = l₂ ↔ l₁.length = l₂.length ∧ ∀ (n : ℕ) (h₁ : n < l₁.length) (h₂ : n < l₂.length), l₁.get ⟨n, h₁⟩ = l₂.get ⟨n, h₂⟩",
"usedConstants": [
"List.get",
"Fin.mk",
"List.ext_get",
"List",
"And",
"Nat",
"And.intro",
"LT.lt",... | constructor
· rintro rfl
exact ⟨rfl, fun _ _ _ ↦ rfl⟩
· intro ⟨h₁, h₂⟩
exact ext_get h₁ h₂ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 676,
"column": 30
} | {
"line": 676,
"column": 44
} | [
{
"pp": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nl✝ l₁ l₂ l : List α\ni j : ℕ\nh : i ≠ j\na : α\nhj : j < (l.set i a).length\n⊢ j < l.length",
"usedConstants": [
"congrArg",
"Eq.mp",
"List.set",
"Nat",
"LT.lt",
"instLTNat",
"List.length",
"List.lengt... | simpa using hj | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Data.List.Basic | {
"line": 676,
"column": 30
} | {
"line": 676,
"column": 44
} | [
{
"pp": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nl✝ l₁ l₂ l : List α\ni j : ℕ\nh : i ≠ j\na : α\nhj : j < (l.set i a).length\n⊢ j < l.length",
"usedConstants": [
"congrArg",
"Eq.mp",
"List.set",
"Nat",
"LT.lt",
"instLTNat",
"List.length",
"List.lengt... | simpa using hj | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Basic | {
"line": 676,
"column": 30
} | {
"line": 676,
"column": 44
} | [
{
"pp": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nl✝ l₁ l₂ l : List α\ni j : ℕ\nh : i ≠ j\na : α\nhj : j < (l.set i a).length\n⊢ j < l.length",
"usedConstants": [
"congrArg",
"Eq.mp",
"List.set",
"Nat",
"LT.lt",
"instLTNat",
"List.length",
"List.lengt... | simpa using hj | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 839,
"column": 2
} | {
"line": 839,
"column": 56
} | [
{
"pp": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nl : List ι\nf : α → β → γ\nop₁ : ι → α → α\nop₂ : ι → β → β\nop₃ : ι → γ → γ\nb : β\nh : ∀ (a : α) (b : β) (i : ι), f (op₁ i a) (op₂ i b) = op₃ i (f a b)\n⊢ ∀ (a : α), foldr op₃ (f a b) l = f (foldr op₁ a l) (foldr op₂ b l)",
"usedConstants": [
... | induction l <;> intros <;> [rfl; simp only [*, foldr]] | Batteries.Tactic._aux_Batteries_Tactic_SeqFocus___macroRules_Batteries_Tactic_seq_focus_1 | Batteries.Tactic.seq_focus |
Mathlib.Data.Rat.Cast.Defs | {
"line": 118,
"column": 40
} | {
"line": 118,
"column": 56
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\nn : ℕ\n⊢ ↑↑n = ↑n",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
"AddMonoidWithOne.toNatCast",
"DivisionRing.toRing",
"Int",
"Add... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Defs | {
"line": 152,
"column": 67
} | {
"line": 152,
"column": 83
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\na b : ℤ\nb0 : ↑b ≠ 0\nb0' : b ≠ 0\nn : ℤ\nd : ℕ\nh : d ≠ 0\nc : n.natAbs.Coprime d\ne : a /. b = { num := n, den := d, den_nz := h, reduced := c }\nd0 : ↑d = 0\ndd : ↑(a /. b).den ∣ b\nk : ℤ\nke : b = ↑d * k\n⊢ ↑↑d * ↑k = ↑d * ↑k",
"usedConstants": [
"Int... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Defs | {
"line": 158,
"column": 34
} | {
"line": 158,
"column": 50
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\na b : ℤ\nb0 : ↑b ≠ 0\nb0' : b ≠ 0\nn : ℤ\nd : ℕ\nh : d ≠ 0\nc : n.natAbs.Coprime d\ne : a /. b = n /. ↑d\nd0 : ↑d ≠ 0\nthis : ↑a * ↑↑d = ↑n * ↑b\n⊢ ↑{ num := n, den := d, den_nz := h, reduced := c } = ↑a / ↑b",
"usedConstants": [
"Int.cast",
"Int.ca... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Defs | {
"line": 164,
"column": 51
} | {
"line": 164,
"column": 67
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\na : ℤ\nb : ℕ\nhb : ↑b ≠ 0\n⊢ ↑a / ↑↑b = ↑a / ↑b",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"instHDiv",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"DivisionRing.toDivInvMonoid",
"id",
... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Defs | {
"line": 164,
"column": 75
} | {
"line": 164,
"column": 91
} | [
{
"pp": "case b0\nα : Type u_3\ninst✝ : DivisionRing α\na : ℤ\nb : ℕ\nhb : ↑b ≠ 0\n⊢ ↑↑b ≠ 0",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Ring.toNonAssocRing",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toMulZeroC... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Defs | {
"line": 192,
"column": 63
} | {
"line": 192,
"column": 79
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\nq : ℚ\nhq : ↑q.num ≠ 0\n⊢ ↑↑q.den / ↑q.num = ↑q.den / ↑q.num",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Rat.num",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"congrArg",
"AddGroupWithOne.toA... | Int.cast_natCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.CompleteLattice.Basic | {
"line": 462,
"column": 23
} | {
"line": 464,
"column": 9
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\nb : β\nf : (x : β) → b = x → α\nc : β\n⊢ ∀ (j : b = c), f c j ≤ f b ⋯",
"usedConstants": [
"le_refl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.rec",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",... | by
rintro rfl
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteLattice.Basic | {
"line": 542,
"column": 37
} | {
"line": 545,
"column": 74
} | [
{
"pp": "α : Type u_1\ninst✝¹ : CompleteLattice α\nι : Type u_8\ninst✝ : Preorder ι\nf : ι → α\n⊢ ⨆ i, ⨆ j, ⨆ (_ : j ≤ i), f j = ⨆ i, f i",
"usedConstants": [
"iSup₂_le",
"le_rfl",
"iSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"le_iSup",
"LE.le",
"Comple... | by
apply le_antisymm
· exact iSup_le fun _ ↦ iSup₂_le fun _ _ ↦ le_iSup _ _
· exact iSup_le fun j ↦ le_iSup_of_le j (le_iSup₂_of_le j le_rfl le_rfl) | [anonymous] | Lean.Parser.Term.byTactic |
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