module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 487,
"column": 2
} | {
"line": 487,
"column": 28
} | {
"line": 487,
"column": 29
} | [
{
"pp": "R : Type u\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\na b : R\ninst✝ : PosMulStrictMono R\nh : ∀ (n : ℕ), 0 ≤ a * b ^ n\nthis : 0 ≤ a\nha : 0 < a\n⊢ 0 ≤ a * b",
"ppTerm": "?m.78",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\na b : R\ninst✝ : PosMulStrictMono R\nh : ∀ (n : ℕ), 0 ≤ a * b ^ n\nthis : 0 ≤ a\nha : 0 < a\n⊢ 0 ≤ a * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 505,
"column": 2
} | {
"line": 505,
"column": 31
} | {
"line": 506,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝⁶ : Semiring R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : ExistsAddOfLE R\ninst✝³ : MulPosStrictMono R\ninst✝² : PosMulStrictMono R\ninst✝¹ : AddLeftMono R\ninst✝ : AddLeftReflectLE R\na b c : R\n⊢ 0 ≤ a * b ∨ 0 ≤ b * c ∨ 0 ≤ c * a",
"ppTerm": "?m.37",
"assigned": true,
"usedConstan... | [
"R : Type u\ninst✝⁶ : Semiring R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : ExistsAddOfLE R\ninst✝³ : MulPosStrictMono R\ninst✝² : PosMulStrictMono R\ninst✝¹ : AddLeftMono R\ninst✝ : AddLeftReflectLE R\na b c : R\n⊢ (0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0) ∨ (0 ≤ b ∧ 0 ≤ c ∨ b ≤ 0 ∧ c ≤ 0) ∨ 0 ≤ c ∧ 0 ≤ a ∨ c ≤ 0 ∧ a ≤ 0"
] | iterate 3 rw [mul_nonneg_iff] | Lean.Parser.Tactic._aux_Init_TacticsExtra___macroRules_Lean_Parser_Tactic_tacticIterate_____1 | Lean.Parser.Tactic.tacticIterate____ |
Mathlib.Logic.Embedding.Basic | {
"line": 355,
"column": 23
} | {
"line": 355,
"column": 66
} | {
"line": 355,
"column": 67
} | [
{
"pp": "α : Sort u\nβ : Sort v\nγ : Sort w\ninst✝ : Inhabited γ\ne : α ↪ β\nf₁ f₂ : α → γ\nh : (fun f ↦ extend (⇑e) f default) f₁ = (fun f ↦ extend (⇑e) f default) f₂\nx : α\n⊢ f₁ x = f₂ x",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u\nβ : Sort v\nγ : Sort w\ninst✝ : Inhabited γ\ne : α ↪ β\nf₁ f₂ : α → γ\nh : (fun f ↦ extend (⇑e) f default) f₁ = (fun f ↦ extend (⇑e) f default) f₂\nx : α\n⊢ f₁ x = f₂ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 629,
"column": 30
} | {
"line": 629,
"column": 51
} | {
"line": 629,
"column": 52
} | [
{
"pp": "R : Type u\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\ninst✝² : ExistsAddOfLE R\ninst✝¹ : PosMulMono R\ninst✝ : AddLeftMono R\na : R\n⊢ 0 ≤ a * a",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\ninst✝² : ExistsAddOfLE R\ninst✝¹ : PosMulMono R\ninst✝ : AddLeftMono R\na : R\n⊢ 0 ≤ a * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 633,
"column": 20
} | {
"line": 633,
"column": 46
} | {
"line": 633,
"column": 47
} | [
{
"pp": "R : Type u\nα : Type u_1\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\na b c : R\ninst✝² : ExistsAddOfLE R\ninst✝¹ : PosMulMono R\ninst✝ : AddLeftMono R\n⊢ 0 ≤ 1",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\nα : Type u_1\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\na b c : R\ninst✝² : ExistsAddOfLE R\ninst✝¹ : PosMulMono R\ninst✝ : AddLeftMono R\n⊢ 0 ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 326,
"column": 2
} | {
"line": 326,
"column": 28
} | {
"line": 326,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosMono α\nhb : 0 ≤ b\nh : a ≤ 1\n⊢ a * b ≤ b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosMono α\nhb : 0 ≤ b\nh : a ≤ 1\n⊢ a * b ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 329,
"column": 2
} | {
"line": 329,
"column": 28
} | {
"line": 329,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosMono α\nhb : 0 ≤ b\nh : 1 ≤ a\n⊢ b ≤ a * b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosMono α\nhb : 0 ≤ b\nh : 1 ≤ a\n⊢ b ≤ a * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 332,
"column": 2
} | {
"line": 332,
"column": 28
} | {
"line": 332,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulMono α\nha : 0 ≤ a\nh : b ≤ 1\n⊢ a * b ≤ a",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulMono α\nha : 0 ≤ a\nh : b ≤ 1\n⊢ a * b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 335,
"column": 2
} | {
"line": 335,
"column": 28
} | {
"line": 335,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulMono α\nha : 0 ≤ a\nh : 1 ≤ b\n⊢ a ≤ a * b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulMono α\nha : 0 ≤ a\nh : 1 ≤ b\n⊢ a ≤ a * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 338,
"column": 2
} | {
"line": 338,
"column": 28
} | {
"line": 338,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosStrictMono α\nhb : 0 < b\nh : a < 1\n⊢ a * b < b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosStrictMono α\nhb : 0 < b\nh : a < 1\n⊢ a * b < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 341,
"column": 2
} | {
"line": 341,
"column": 28
} | {
"line": 341,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosStrictMono α\nhb : 0 < b\nh : 1 < a\n⊢ b < a * b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : MulPosStrictMono α\nhb : 0 < b\nh : 1 < a\n⊢ b < a * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 344,
"column": 2
} | {
"line": 344,
"column": 28
} | {
"line": 344,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulStrictMono α\nha : 0 < a\nh : b < 1\n⊢ a * b < a",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulStrictMono α\nha : 0 < a\nh : b < 1\n⊢ a * b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 347,
"column": 2
} | {
"line": 347,
"column": 28
} | {
"line": 347,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulStrictMono α\nha : 0 < a\nh : 1 < b\n⊢ a < a * b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : MulOneClass α\ninst✝² : Zero α\na b : α\ninst✝¹ : Preorder α\ninst✝ : PosMulStrictMono α\nha : 0 < a\nh : 1 < b\n⊢ a < a * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 676,
"column": 13
} | {
"line": 676,
"column": 45
} | {
"line": 676,
"column": 46
} | [
{
"pp": "R : Type u\ninst✝³ : CommSemiring R\ninst✝² : LinearOrder R\na d : R\ninst✝¹ : PosMulMono R\ninst✝ : MulPosMono R\nb c : R\nha : 0 ≤ a\nhd : 0 ≤ d\nba : b * a ≤ max d b * max c a\ncd : c * d ≤ max a c * max b d\n⊢ a * b ≤ max a c * max d b",
"ppTerm": "?m.90",
"assigned": false,
"usedConsta... | [
"R : Type u\ninst✝³ : CommSemiring R\ninst✝² : LinearOrder R\na d : R\ninst✝¹ : PosMulMono R\ninst✝ : MulPosMono R\nb c : R\nha : 0 ≤ a\nhd : 0 ≤ d\nba : b * a ≤ max d b * max c a\ncd : c * d ≤ max a c * max b d\n⊢ a * b ≤ max a c * max d b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 462,
"column": 2
} | {
"line": 462,
"column": 28
} | {
"line": 462,
"column": 29
} | [
{
"pp": "M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : Preorder M₀\na : M₀\nn : ℕ\ninst✝¹ : ZeroLEOneClass M₀\ninst✝ : PosMulMono M₀\nha : 1 ≤ a\nhn : n ≠ 0\n⊢ a ≤ a ^ n",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : Preorder M₀\na : M₀\nn : ℕ\ninst✝¹ : ZeroLEOneClass M₀\ninst✝ : PosMulMono M₀\nha : 1 ≤ a\nhn : n ≠ 0\n⊢ a ≤ a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 676,
"column": 54
} | {
"line": 676,
"column": 86
} | {
"line": 676,
"column": 87
} | [
{
"pp": "R : Type u\ninst✝³ : CommSemiring R\ninst✝² : LinearOrder R\na d : R\ninst✝¹ : PosMulMono R\ninst✝ : MulPosMono R\nb c : R\nha : 0 ≤ a\nhd : 0 ≤ d\nba : b * a ≤ max d b * max c a\ncd : c * d ≤ max a c * max b d\n⊢ d * c ≤ max a c * max d b",
"ppTerm": "?m.91",
"assigned": false,
"usedConsta... | [
"R : Type u\ninst✝³ : CommSemiring R\ninst✝² : LinearOrder R\na d : R\ninst✝¹ : PosMulMono R\ninst✝ : MulPosMono R\nb c : R\nha : 0 ≤ a\nhd : 0 ≤ d\nba : b * a ≤ max d b * max c a\ncd : c * d ≤ max a c * max b d\n⊢ d * c ≤ max a c * max d b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 473,
"column": 12
} | {
"line": 473,
"column": 23
} | {
"line": 473,
"column": 24
} | [
{
"pp": "M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : Preorder M₀\na b : M₀\ninst✝¹ : PosMulMono M₀\ninst✝ : MulPosMono M₀\nha : 0 ≤ a\nhab : a ≤ b\n⊢ a ^ 1 ≤ b ^ 1",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Preorder.toLE",
"id",
... | [
"M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : Preorder M₀\na b : M₀\ninst✝¹ : PosMulMono M₀\ninst✝ : MulPosMono M₀\nha : 0 ≤ a\nhab : a ≤ b\n⊢ a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 474,
"column": 16
} | {
"line": 475,
"column": 11
} | {
"line": 475,
"column": 12
} | [
{
"pp": "M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : Preorder M₀\na b : M₀\ninst✝¹ : PosMulMono M₀\ninst✝ : MulPosMono M₀\nha : 0 ≤ a\nhab : a ≤ b\nn : ℕ\n⊢ a ^ (n + 2) ≤ b ^ (n + 2)",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.to... | [
"M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : Preorder M₀\na b : M₀\ninst✝¹ : PosMulMono M₀\ninst✝ : MulPosMono M₀\nha : 0 ≤ a\nhab : a ≤ b\nn : ℕ\n⊢ a * (a * a ^ n) ≤ b * (b * b ^ n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 683,
"column": 2
} | {
"line": 684,
"column": 9
} | {
"line": 684,
"column": 10
} | [
{
"pp": "R : Type u\ninst✝⁵ : CommSemiring R\ninst✝⁴ : LinearOrder R\ninst✝³ : ExistsAddOfLE R\ninst✝² : MulPosStrictMono R\ninst✝¹ : AddLeftReflectLE R\ninst✝ : AddLeftMono R\na b : R\n⊢ 2 * a * b ≤ a ^ 2 + b ^ 2",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"add_mul",
"Eq.m... | [
"R : Type u\ninst✝⁵ : CommSemiring R\ninst✝⁴ : LinearOrder R\ninst✝³ : ExistsAddOfLE R\ninst✝² : MulPosStrictMono R\ninst✝¹ : AddLeftReflectLE R\ninst✝ : AddLeftMono R\na b : R\n⊢ a * b + a * b ≤ a * a + b * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 523,
"column": 2
} | {
"line": 523,
"column": 13
} | {
"line": 523,
"column": 14
} | [
{
"pp": "M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na b : M₀\ninst✝ : MulPosStrictMono M₀\nha : 0 < a\nhb : 1 < b\n⊢ a < b * a",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na b : M₀\ninst✝ : MulPosStrictMono M₀\nha : 0 < a\nhb : 1 < b\n⊢ a < b * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 526,
"column": 2
} | {
"line": 526,
"column": 13
} | {
"line": 526,
"column": 14
} | [
{
"pp": "M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na b : M₀\ninst✝ : PosMulStrictMono M₀\nha : 0 < a\nhb : 1 < b\n⊢ a < a * b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na b : M₀\ninst✝ : PosMulStrictMono M₀\nha : 0 < a\nhb : 1 < b\n⊢ a < a * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 532,
"column": 2
} | {
"line": 532,
"column": 23
} | {
"line": 532,
"column": 24
} | [
{
"pp": "M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\ninst✝ : PosMulStrictMono M₀\nha : 0 < a\n⊢ 0 < a ^ 2",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg... | [
"M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\ninst✝ : PosMulStrictMono M₀\nha : 0 < a\n⊢ 0 < a * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 538,
"column": 12
} | {
"line": 538,
"column": 23
} | {
"line": 538,
"column": 24
} | [
{
"pp": "M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\ninst✝ : PosMulStrictMono M₀\nha : 0 < a\n⊢ 0 < a ^ (0 + 1)",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"... | [
"M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\ninst✝ : PosMulStrictMono M₀\nha : 0 < a\n⊢ 0 < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 548,
"column": 15
} | {
"line": 548,
"column": 26
} | {
"line": 548,
"column": 27
} | [
{
"pp": "M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na b : M₀\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : MulPosMono M₀\nhab : a < b\nha : 0 ≤ a\nx✝ : 1 ≠ 0\n⊢ a ^ 1 < b ^ 1",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"co... | [
"M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na b : M₀\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : MulPosMono M₀\nhab : a < b\nha : 0 ≤ a\nx✝ : 1 ≠ 0\n⊢ a < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 550,
"column": 4
} | {
"line": 550,
"column": 31
} | {
"line": 550,
"column": 32
} | [
{
"pp": "M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na b : M₀\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : MulPosMono M₀\nhab : a < b\nha : 0 ≤ a\nn : ℕ\nx✝ : n + 2 ≠ 0\n⊢ a ^ (n + 2) < b ^ (n + 2)",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pr... | [
"M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na b : M₀\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : MulPosMono M₀\nhab : a < b\nha : 0 ≤ a\nn : ℕ\nx✝ : n + 2 ≠ 0\n⊢ a ^ n * a * a < b ^ n * b * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 565,
"column": 4
} | {
"line": 565,
"column": 40
} | {
"line": 565,
"column": 41
} | [
{
"pp": "M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na : M₀\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : ZeroLEOneClass M₀\nh : 1 < a\nn : ℕ\n⊢ a ^ n < a ^ (n + 1)",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"HMul.hMul",
... | [
"M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na : M₀\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : ZeroLEOneClass M₀\nh : 1 < a\nn : ℕ\n⊢ a ^ n < a ^ n * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 577,
"column": 2
} | {
"line": 577,
"column": 28
} | {
"line": 577,
"column": 29
} | [
{
"pp": "M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na : M₀\nm : ℕ\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : ZeroLEOneClass M₀\nh : 1 < a\nhm : 1 < m\n⊢ a < a ^ m",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M₀ : Type u_2\ninst✝³ : MonoidWithZero M₀\ninst✝² : PartialOrder M₀\na : M₀\nm : ℕ\ninst✝¹ : PosMulStrictMono M₀\ninst✝ : ZeroLEOneClass M₀\nh : 1 < a\nhm : 1 < m\n⊢ a < a ^ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 584,
"column": 4
} | {
"line": 584,
"column": 40
} | {
"line": 584,
"column": 41
} | [
{
"pp": "M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\ninst✝ : PosMulStrictMono M₀\nh₀ : 0 < a\nh₁ : a < 1\nn : ℕ\nthis : ZeroLEOneClass M₀\n⊢ a ^ (n + 1) < a ^ n",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"HM... | [
"M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\ninst✝ : PosMulStrictMono M₀\nh₀ : 0 < a\nh₁ : a < 1\nn : ℕ\nthis : ZeroLEOneClass M₀\n⊢ a ^ n * a < a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 596,
"column": 2
} | {
"line": 596,
"column": 28
} | {
"line": 596,
"column": 29
} | [
{
"pp": "M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\nn : ℕ\ninst✝ : PosMulStrictMono M₀\nh₀ : 0 < a\nh₁ : a < 1\nhn : 1 < n\n⊢ a ^ n < a",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : PartialOrder M₀\na : M₀\nn : ℕ\ninst✝ : PosMulStrictMono M₀\nh₀ : 0 < a\nh₁ : a < 1\nhn : 1 < n\n⊢ a ^ n < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 828,
"column": 41
} | {
"line": 828,
"column": 74
} | {
"line": 828,
"column": 75
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : Preorder G₀\ninst✝ : ZeroLEOneClass G₀\na : G₀\n⊢ a * a⁻¹ ≤ 1",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : Preorder G₀\ninst✝ : ZeroLEOneClass G₀\na : G₀\n⊢ a * a⁻¹ ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 828,
"column": 41
} | {
"line": 828,
"column": 92
} | {
"line": 830,
"column": 0
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : Preorder G₀\ninst✝ : ZeroLEOneClass G₀\na : G₀\n⊢ a * a⁻¹ ≤ 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"DivInvMonoid.toInv",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"... | [] | simpa only [div_eq_mul_inv] using div_self_le_one a | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 828,
"column": 41
} | {
"line": 828,
"column": 92
} | {
"line": 830,
"column": 0
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : Preorder G₀\ninst✝ : ZeroLEOneClass G₀\na : G₀\n⊢ a * a⁻¹ ≤ 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"DivInvMonoid.toInv",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"... | [] | simpa only [div_eq_mul_inv] using div_self_le_one a | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 828,
"column": 41
} | {
"line": 828,
"column": 92
} | {
"line": 830,
"column": 0
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : Preorder G₀\ninst✝ : ZeroLEOneClass G₀\na : G₀\n⊢ a * a⁻¹ ≤ 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"DivInvMonoid.toInv",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"... | [] | simpa only [div_eq_mul_inv] using div_self_le_one a | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 876,
"column": 4
} | {
"line": 876,
"column": 24
} | {
"line": 876,
"column": 25
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\ninst✝ : MulPosMono G₀\na : G₀\nha : 0 < a\nb c : G₀\nh : (fun x y ↦ y * ↑x) ⟨a, ha⟩ b ≤ (fun x y ↦ y * ↑x) ⟨a, ha⟩ c\n⊢ b ≤ c",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"us... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\ninst✝ : MulPosMono G₀\na : G₀\nha : 0 < a\nb c : G₀\nh : (fun x y ↦ y * ↑x) ⟨a, ha⟩ b ≤ (fun x y ↦ y * ↑x) ⟨a, ha⟩ c\n⊢ b ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 901,
"column": 55
} | {
"line": 901,
"column": 66
} | {
"line": 901,
"column": 67
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ 1 ≤ a⁻¹ ↔ a ≤ 1",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ 1 ≤ a⁻¹ ↔ a ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 902,
"column": 55
} | {
"line": 902,
"column": 66
} | {
"line": 902,
"column": 67
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ a⁻¹ ≤ 1 ↔ 1 ≤ a",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ a⁻¹ ≤ 1 ↔ 1 ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 910,
"column": 4
} | {
"line": 910,
"column": 15
} | {
"line": 910,
"column": 16
} | [
{
"pp": "case inl\nG₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na b : G₀\nhb : 0 ≤ b\nhc : 0 ≤ 0\nh : a ≤ 0⁻¹ * b\n⊢ 0 * a ≤ b",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"HM... | [
"case inl\nG₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na b : G₀\nhb : 0 ≤ b\nhc : 0 ≤ 0\nh : a ≤ 0⁻¹ * b\n⊢ 0 ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 935,
"column": 55
} | {
"line": 935,
"column": 66
} | {
"line": 935,
"column": 67
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ 1 < a⁻¹ ↔ a < 1",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ 1 < a⁻¹ ↔ a < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 936,
"column": 55
} | {
"line": 936,
"column": 66
} | {
"line": 936,
"column": 67
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ a⁻¹ < 1 ↔ 1 < a",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : PosMulReflectLT G₀\na : G₀\nha : 0 < a\n⊢ a⁻¹ < 1 ↔ 1 < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.RelIso.Basic | {
"line": 193,
"column": 18
} | {
"line": 193,
"column": 53
} | {
"line": 193,
"column": 54
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\nf : α → β\nhf : Surjective f\no : ∀ {a b : α}, r a b ↔ s (f a) (f b)\na✝ b✝ : β\nh : s a✝ b✝\n⊢ r (surjInv hf a✝) (surjInv hf b✝)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"α : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\nf : α → β\nhf : Surjective f\no : ∀ {a b : α}, r a b ↔ s (f a) (f b)\na✝ b✝ : β\nh : s a✝ b✝\n⊢ s a✝ b✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 999,
"column": 63
} | {
"line": 999,
"column": 74
} | {
"line": 999,
"column": 75
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 ≤ a\nhn : 0 ≤ n\n⊢ 1 ≤ a ^ n",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 ≤ a\nhn : 0 ≤ n\n⊢ 1 ≤ a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1002,
"column": 2
} | {
"line": 1002,
"column": 13
} | {
"line": 1002,
"column": 14
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a ≤ 1\nhn : 0 ≤ n\n⊢ a ^ n ≤ 1",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a ≤ 1\nhn : 0 ≤ n\n⊢ a ^ n ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1005,
"column": 2
} | {
"line": 1005,
"column": 13
} | {
"line": 1005,
"column": 14
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 ≤ a\nhn : n ≤ 0\n⊢ a ^ n ≤ 1",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 ≤ a\nhn : n ≤ 0\n⊢ a ^ n ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1008,
"column": 2
} | {
"line": 1008,
"column": 13
} | {
"line": 1008,
"column": 14
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a ≤ 1\nhn : n ≤ 0\n⊢ 1 ≤ a ^ n",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a ≤ 1\nhn : n ≤ 0\n⊢ 1 ≤ a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1018,
"column": 2
} | {
"line": 1018,
"column": 13
} | {
"line": 1018,
"column": 14
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 < a\nhn : 0 < n\n⊢ 1 < a ^ n",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 < a\nhn : 0 < n\n⊢ 1 < a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1021,
"column": 2
} | {
"line": 1021,
"column": 13
} | {
"line": 1021,
"column": 14
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a < 1\nhn : 0 < n\n⊢ a ^ n < 1",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a < 1\nhn : 0 < n\n⊢ a ^ n < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1024,
"column": 2
} | {
"line": 1024,
"column": 13
} | {
"line": 1024,
"column": 14
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 < a\nhn : n < 0\n⊢ a ^ n < 1",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha : 1 < a\nhn : n < 0\n⊢ a ^ n < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1027,
"column": 2
} | {
"line": 1027,
"column": 13
} | {
"line": 1027,
"column": 14
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a < 1\nhn : n < 0\n⊢ 1 < a ^ n",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nn : ℤ\nha₀ : 0 < a\nha₁ : a < 1\nhn : n < 0\n⊢ 1 < a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.RelIso.Basic | {
"line": 478,
"column": 47
} | {
"line": 478,
"column": 62
} | {
"line": 478,
"column": 63
} | [
{
"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\ninst✝¹ : Std.Trichotomous r\ninst✝ : Std.Asymm s\nf : α → β\nH : ∀ (a b : α), r a b → s (f a) (f b)\nthis : Std.Irrefl s\na b : α\ne : f a = f b\nh : r a b\n⊢ s (f a) (f a)",
... | [
"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\ninst✝¹ : Std.Trichotomous r\ninst✝ : Std.Asymm s\nf : α → β\nH : ∀ (a b : α), r a b → s (f a) (f b)\nthis : Std.Irrefl s\na b : α\ne : f a = f b\nh : r a b\n⊢ s (f b) (f b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.RelIso.Basic | {
"line": 479,
"column": 47
} | {
"line": 479,
"column": 62
} | {
"line": 479,
"column": 63
} | [
{
"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\ninst✝¹ : Std.Trichotomous r\ninst✝ : Std.Asymm s\nf : α → β\nH : ∀ (a b : α), r a b → s (f a) (f b)\nthis : Std.Irrefl s\na b : α\ne : f a = f b\nh : r b a\n⊢ s (f b) (f b)",
... | [
"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\ninst✝¹ : Std.Trichotomous r\ninst✝ : Std.Asymm s\nf : α → β\nH : ∀ (a b : α), r a b → s (f a) (f b)\nthis : Std.Irrefl s\na b : α\ne : f a = f b\nh : r b a\n⊢ s (f b) (f b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1074,
"column": 24
} | {
"line": 1074,
"column": 35
} | {
"line": 1074,
"column": 36
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\ninst✝ : MulPosMono G₀\nn : ℕ\n⊢ MonotoneOn (fun a ↦ a ^ ↑n) {a | 0 ≤ a}",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"GroupWithZero.toMon... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\ninst✝ : MulPosMono G₀\nn : ℕ\n⊢ MonotoneOn (fun a ↦ a ^ n) {a | 0 ≤ a}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1077,
"column": 27
} | {
"line": 1077,
"column": 38
} | {
"line": 1077,
"column": 39
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\ninst✝ : MulPosMono G₀\nn : ℕ\nhn : 0 < ↑n\n⊢ StrictMonoOn (fun a ↦ a ^ ↑n) {a | 0 ≤ a}",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"Grou... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\ninst✝ : MulPosMono G₀\nn : ℕ\nhn : 0 < ↑n\n⊢ StrictMonoOn (fun a ↦ a ^ n) {a | 0 ≤ a}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1161,
"column": 2
} | {
"line": 1161,
"column": 36
} | {
"line": 1163,
"column": 0
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : MulPosReflectLT G₀\na b : G₀\nha : 0 < a\n⊢ a⁻¹ < b ↔ 1 < b * a",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"Preorder... | [] | rw [← mul_inv_lt_iff₀ ha, one_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1161,
"column": 2
} | {
"line": 1161,
"column": 36
} | {
"line": 1163,
"column": 0
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : MulPosReflectLT G₀\na b : G₀\nha : 0 < a\n⊢ a⁻¹ < b ↔ 1 < b * a",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"Preorder... | [] | rw [← mul_inv_lt_iff₀ ha, one_mul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1161,
"column": 2
} | {
"line": 1161,
"column": 36
} | {
"line": 1163,
"column": 0
} | [
{
"pp": "G₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : MulPosReflectLT G₀\na b : G₀\nha : 0 < a\n⊢ a⁻¹ < b ↔ 1 < b * a",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"Preorder... | [] | rw [← mul_inv_lt_iff₀ ha, one_mul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1172,
"column": 4
} | {
"line": 1172,
"column": 15
} | {
"line": 1172,
"column": 16
} | [
{
"pp": "case inl\nG₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : MulPosReflectLT G₀\na b : G₀\nhb : 0 ≤ b\nhc : 0 ≤ 0\nh : a ≤ b * 0⁻¹\n⊢ a * 0 ≤ b",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"HM... | [
"case inl\nG₀ : Type u_3\ninst✝² : GroupWithZero G₀\ninst✝¹ : PartialOrder G₀\ninst✝ : MulPosReflectLT G₀\na b : G₀\nhb : 0 ≤ b\nhc : 0 ≤ 0\nh : a ≤ b * 0⁻¹\n⊢ 0 ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1293,
"column": 24
} | {
"line": 1293,
"column": 45
} | {
"line": 1293,
"column": 45
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\ninst✝ : MulPosReflectLT G₀\na b c d : G₀\nhac : a < c\nhdb : d ≤ b\nhc : 0 ≤ c\nhd : 0 < d\n⊢ b⁻¹ ≤ d⁻¹",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"inv_anti₀"
],
"us... | [] | by gcongr; assumption | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 1360,
"column": 2
} | {
"line": 1360,
"column": 13
} | {
"line": 1360,
"column": 14
} | [
{
"pp": "case inr\nG₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : LinearOrder G₀\na : G₀\ninst✝¹ : PosMulStrictMono G₀\ninst✝ : ZeroLEOneClass G₀\nha₀✝ : 0 ≤ a\nha₁ : a ≠ 1\nn : ℤ\nha₀ : 0 < a\n⊢ a ^ n = 1 ↔ n = 0",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"case inr\nG₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : LinearOrder G₀\na : G₀\ninst✝¹ : PosMulStrictMono G₀\ninst✝ : ZeroLEOneClass G₀\nha₀✝ : 0 ≤ a\nha₁ : a ≠ 1\nn : ℤ\nha₀ : 0 < a\n⊢ a ^ n = 1 ↔ n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Defs | {
"line": 87,
"column": 44
} | {
"line": 87,
"column": 64
} | {
"line": 87,
"column": 65
} | [
{
"pp": "R : Type u_1\ninst✝³ : Ring R\ninst✝² : PartialOrder R\ninst✝¹ : IsOrderedRing R\ninst✝ : Archimedean R\nx : R\nn : ℤ\nh : -x ≤ ↑n\n⊢ ↑(-n) ≤ x",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"Eq.m... | [
"R : Type u_1\ninst✝³ : Ring R\ninst✝² : PartialOrder R\ninst✝¹ : IsOrderedRing R\ninst✝ : Archimedean R\nx : R\nn : ℤ\nh : -x ≤ ↑n\n⊢ -x ≤ ↑n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 13
} | {
"line": 80,
"column": 14
} | [
{
"pp": "M : Type u_3\ninst✝² : Monoid M\ninst✝¹ : Preorder M\ninst✝ : MulLeftMono M\na : M\nn : ℕ\nha : 1 ≤ a\nhn : n ≠ 0\n⊢ a ≤ a ^ n",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_3\ninst✝² : Monoid M\ninst✝¹ : Preorder M\ninst✝ : MulLeftMono M\na : M\nn : ℕ\nha : 1 ≤ a\nhn : n ≠ 0\n⊢ a ≤ a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 114,
"column": 87
} | {
"line": 117,
"column": 56
} | {
"line": 119,
"column": 0
} | [
{
"pp": "M : Type u_3\ninst✝² : Monoid M\ninst✝¹ : Preorder M\ninst✝ : MulRightMono M\nn : ℕ\nx : M\nhn : 0 < n\nh : x < 1\n⊢ x ^ n < 1",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Preorder.toLT",
"HMul.hMul",
"Monoid.toMulOneClas... | [] | by
rcases Nat.exists_eq_succ_of_ne_zero hn.ne' with ⟨k, rfl⟩
rw [pow_succ]
exact mul_lt_one_of_le_of_lt (pow_le_one_of_le h.le) h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 144,
"column": 4
} | {
"line": 144,
"column": 31
} | {
"line": 144,
"column": 32
} | [
{
"pp": "β : Type u_1\nM : Type u_3\ninst✝⁴ : Monoid M\ninst✝³ : Preorder M\ninst✝² : Preorder β\ninst✝¹ : MulLeftStrictMono M\ninst✝ : MulRightStrictMono M\nf : β → M\nhf : StrictMono f\nn : ℕ\nx✝ : n.succ.succ ≠ 0\n⊢ StrictMono fun x ↦ f x ^ n.succ.succ",
"ppTerm": "?m.36",
"assigned": true,
"used... | [
"β : Type u_1\nM : Type u_3\ninst✝⁴ : Monoid M\ninst✝³ : Preorder M\ninst✝² : Preorder β\ninst✝¹ : MulLeftStrictMono M\ninst✝ : MulRightStrictMono M\nf : β → M\nhf : StrictMono f\nn : ℕ\nx✝ : n.succ.succ ≠ 0\n⊢ StrictMono fun x ↦ f x ^ n * f x * f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 169,
"column": 12
} | {
"line": 169,
"column": 23
} | {
"line": 169,
"column": 24
} | [
{
"pp": "β : Type u_1\nM : Type u_3\ninst✝⁴ : Monoid M\ninst✝³ : Preorder M\ninst✝² : Preorder β\ninst✝¹ : MulLeftMono M\ninst✝ : MulRightMono M\nf : β → M\nhf : Monotone f\n⊢ Monotone fun a ↦ f a ^ 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
... | [
"β : Type u_1\nM : Type u_3\ninst✝⁴ : Monoid M\ninst✝³ : Preorder M\ninst✝² : Preorder β\ninst✝¹ : MulLeftMono M\ninst✝ : MulRightMono M\nf : β → M\nhf : Monotone f\n⊢ Monotone fun a ↦ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 253,
"column": 2
} | {
"line": 253,
"column": 13
} | {
"line": 253,
"column": 14
} | [
{
"pp": "M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftMono M\ninst✝ : MulRightMono M\na b c : M\nh : a * b < c ^ 2\n⊢ min a b < c",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Part... | [
"M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftMono M\ninst✝ : MulRightMono M\na b c : M\nh : a * b < c ^ 2\n⊢ a < c ∨ b < c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 257,
"column": 2
} | {
"line": 257,
"column": 13
} | {
"line": 257,
"column": 14
} | [
{
"pp": "M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftMono M\ninst✝ : MulRightMono M\na b c : M\nh : a ^ 2 < b * c\n⊢ a < max b c",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"lt_s... | [
"M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftMono M\ninst✝ : MulRightMono M\na b c : M\nh : a ^ 2 < b * c\n⊢ a < b ∨ a < c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 13
} | {
"line": 274,
"column": 14
} | [
{
"pp": "M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftStrictMono M\ninst✝ : MulRightStrictMono M\na b c : M\nh : a * b ≤ c ^ 2\n⊢ min a b ≤ c",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"PartialOrder.to... | [
"M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftStrictMono M\ninst✝ : MulRightStrictMono M\na b c : M\nh : a * b ≤ c ^ 2\n⊢ a ≤ c ∨ b ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Pow | {
"line": 278,
"column": 2
} | {
"line": 278,
"column": 13
} | {
"line": 278,
"column": 14
} | [
{
"pp": "M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftStrictMono M\ninst✝ : MulRightStrictMono M\na b c : M\nh : a ^ 2 ≤ b * c\n⊢ a ≤ max b c",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"PartialOrder.to... | [
"M : Type u_3\ninst✝³ : Monoid M\ninst✝² : LinearOrder M\ninst✝¹ : MulLeftStrictMono M\ninst✝ : MulRightStrictMono M\na b c : M\nh : a ^ 2 ≤ b * c\n⊢ a ≤ b ∨ a ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Basic | {
"line": 1138,
"column": 17
} | {
"line": 1138,
"column": 33
} | {
"line": 1138,
"column": 34
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type u_5\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α →o β\ng : β →o α\nh₁ : f.comp g = OrderHom.id\nh₂ : g.comp f = OrderHom.id\na✝ b✝ : α\nh :\n { toFun := ⇑f, invFun := ⇑g, left_inv := ⋯, right_inv := ⋯ } a✝ ≤\n { toFun := ⇑f, invFun... | [
"F : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type u_5\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α →o β\ng : β →o α\nh₁ : f.comp g = OrderHom.id\nh₂ : g.comp f = OrderHom.id\na✝ b✝ : α\nh :\n { toFun := ⇑f, invFun := ⇑g, left_inv := ⋯, right_inv := ⋯ } a✝ ≤\n { toFun := ⇑f, invFun := ⇑g, left... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Basic | {
"line": 1178,
"column": 19
} | {
"line": 1178,
"column": 56
} | {
"line": 1178,
"column": 57
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type u_5\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃ β\nh₁ : Monotone ⇑e\nh₂ : Monotone ⇑e.symm\na✝ b✝ : α\nh : e a✝ ≤ e b✝\n⊢ a✝ ≤ b✝",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"F : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type u_5\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃ β\nh₁ : Monotone ⇑e\nh₂ : Monotone ⇑e.symm\na✝ b✝ : α\nh : e a✝ ≤ e b✝\n⊢ a✝ ≤ b✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Basic | {
"line": 1246,
"column": 2
} | {
"line": 1246,
"column": 13
} | {
"line": 1246,
"column": 14
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : SemilatticeInf α\ninst✝ : SemilatticeInf β\nf : α ≃o β\nx y : α\n⊢ f.symm (f.toOrderEmbedding x ⊓ f.toOrderEmbedding y) ≤ f.symm (f.toOrderEmbedding (x ⊓ y))",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"α : Type u_2\nβ : Type u_3\ninst✝¹ : SemilatticeInf α\ninst✝ : SemilatticeInf β\nf : α ≃o β\nx y : α\n⊢ f.symm (f x ⊓ f y) ≤ x ∧ f.symm (f x ⊓ f y) ≤ y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Basic | {
"line": 1306,
"column": 2
} | {
"line": 1307,
"column": 9
} | {
"line": 1307,
"column": 10
} | [
{
"pp": "X : Type u_6\nY : Type u_7\ninst✝² : LinearOrder X\ninst✝¹ : DenselyOrdered X\ninst✝ : Preorder Y\nf : X → Y\nhf : StrictMono f\n⊢ ∀ (a₁ a₂ : ↑(Set.range f)), a₁ < a₂ → ∃ a, a₁ < a ∧ a < a₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Pre... | [
"X : Type u_6\nY : Type u_7\ninst✝² : LinearOrder X\ninst✝¹ : DenselyOrdered X\ninst✝ : Preorder Y\nf : X → Y\nhf : StrictMono f\n⊢ ∀ (a a_1 : X), a < a_1 → ∃ b, a < b ∧ b < a_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Basic | {
"line": 1316,
"column": 19
} | {
"line": 1316,
"column": 30
} | {
"line": 1316,
"column": 31
} | [
{
"pp": "X : Type u_6\nY : Type u_7\nF : Type u_8\ninst✝³ : Preorder X\ninst✝² : Preorder Y\ninst✝¹ : EquivLike F X Y\ninst✝ : OrderIsoClass F X Y\nf : F\nH : DenselyOrdered X\na b : Y\nh : a < b\nc : X\nhc : EquivLike.inv f a < c ∧ c < EquivLike.inv f b\n⊢ a < f c ∧ f c < b",
"ppTerm": "?m.49",
"assign... | [
"X : Type u_6\nY : Type u_7\nF : Type u_8\ninst✝³ : Preorder X\ninst✝² : Preorder Y\ninst✝¹ : EquivLike F X Y\ninst✝ : OrderIsoClass F X Y\nf : F\nH : DenselyOrdered X\na b : Y\nh : a < b\nc : X\nhc : EquivLike.inv f a < c ∧ c < EquivLike.inv f b\n⊢ a < f c ∧ f c < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Basic | {
"line": 1320,
"column": 33
} | {
"line": 1320,
"column": 44
} | {
"line": 1320,
"column": 45
} | [
{
"pp": "X : Type u_6\nY : Type u_7\nF : Type u_8\ninst✝³ : Preorder X\ninst✝² : Preorder Y\ninst✝¹ : EquivLike F X Y\ninst✝ : OrderIsoClass F X Y\nf : F\nH : DenselyOrdered Y\na b : X\nh : a < b\nc : Y\nhc : f a < c ∧ c < f b\n⊢ a < EquivLike.inv f c ∧ EquivLike.inv f c < b",
"ppTerm": "?m.100",
"assig... | [
"X : Type u_6\nY : Type u_7\nF : Type u_8\ninst✝³ : Preorder X\ninst✝² : Preorder Y\ninst✝¹ : EquivLike F X Y\ninst✝ : OrderIsoClass F X Y\nf : F\nH : DenselyOrdered Y\na b : X\nh : a < b\nc : Y\nhc : f a < c ∧ c < f b\n⊢ f a < c ∧ c < f b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Basic | {
"line": 1326,
"column": 2
} | {
"line": 1326,
"column": 62
} | {
"line": 1327,
"column": 2
} | [
{
"pp": "X : Type u_6\nY : Type u_7\nF : Type u_8\ninst✝² : LinearOrder X\ninst✝¹ : Preorder Y\ninst✝ : EquivLike F X Y\nf : F\nhf : StrictAnti ⇑f\n⊢ DenselyOrdered Xᵒᵈ ↔ DenselyOrdered Y",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"OrderDual.instLE",
"RelIso.mk",
"Or... | [
"case refine_2\nX : Type u_6\nY : Type u_7\nF : Type u_8\ninst✝² : LinearOrder X\ninst✝¹ : Preorder Y\ninst✝ : EquivLike F X Y\nf : F\nhf : StrictAnti ⇑f\ne : Xᵒᵈ ≃o Y := { toEquiv := ofDual.trans ↑f, map_rel_iff' := ?refine_1 }\n⊢ DenselyOrdered Xᵒᵈ ↔ DenselyOrdered Y",
"case refine_1\nX : Type u_6\nY : Type u_7... | let e : Xᵒᵈ ≃o Y := ⟨OrderDual.ofDual.trans (f : X ≃ Y), ?_⟩ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Algebra.Order.Group.Abs | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 36
} | {
"line": 61,
"column": 2
} | [
{
"pp": "case inl\nG : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\nab : a ≤ b\n⊢ |a * b|ₘ = |a|ₘ * |b|ₘ ↔ 1 ≤ a ∧ 1 ≤ b ∨ a ≤ 1 ∧ b ≤ 1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Algebra.Order.Group.Abs.0.mabs_mul_... | [] | exact mabs_mul_eq_mul_mabs_le ab | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Group.Abs | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 36
} | {
"line": 61,
"column": 2
} | [
{
"pp": "case inl\nG : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\nab : a ≤ b\n⊢ |a * b|ₘ = |a|ₘ * |b|ₘ ↔ 1 ≤ a ∧ 1 ≤ b ∨ a ≤ 1 ∧ b ≤ 1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Algebra.Order.Group.Abs.0.mabs_mul_... | [] | exact mabs_mul_eq_mul_mabs_le ab | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.Abs | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 36
} | {
"line": 61,
"column": 2
} | [
{
"pp": "case inl\nG : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\nab : a ≤ b\n⊢ |a * b|ₘ = |a|ₘ * |b|ₘ ↔ 1 ≤ a ∧ 1 ≤ b ∨ a ≤ 1 ∧ b ≤ 1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Algebra.Order.Group.Abs.0.mabs_mul_... | [] | exact mabs_mul_eq_mul_mabs_le ab | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Abs | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 41
} | {
"line": 61,
"column": 42
} | [
{
"pp": "case inr\nG : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\nab : b ≤ a\n⊢ |a * b|ₘ = |a|ₘ * |b|ₘ ↔ 1 ≤ a ∧ 1 ≤ b ∨ a ≤ 1 ∧ b ≤ 1",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr\nG : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\nab : b ≤ a\n⊢ |a * b|ₘ = |a|ₘ * |b|ₘ ↔ 1 ≤ a ∧ 1 ≤ b ∨ a ≤ 1 ∧ b ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Abs | {
"line": 78,
"column": 59
} | {
"line": 78,
"column": 70
} | {
"line": 78,
"column": 71
} | [
{
"pp": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\n⊢ |a|ₘ ≤ |b|ₘ * |b * a|ₘ",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\n⊢ |a|ₘ ≤ |b|ₘ * |b * a|ₘ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Abs | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 64
} | {
"line": 144,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b : G\nhb : 1 ≤ b\n⊢ a = b ∨ a = b⁻¹ → |a|ₘ = b",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.t... | [] | rintro (rfl | rfl) <;> simp only [mabs_inv, mabs_of_one_le hb] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 170,
"column": 12
} | {
"line": 170,
"column": 28
} | {
"line": 170,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : MulLeftMono α\na b c : α\nthis : DistribLattice α := CommGroup.toDistribLattice α\n⊢ (b ⊔ c ⊔ (a ⊔ c)) / ((b ⊔ c) ⊓ (a ⊔ c)) * ((b ⊓ c ⊔ a ⊓ c) / (b ⊓ c ⊓ (a ⊓ c))) =\n (b ⊔ a ⊔ c) / (b ⊓ a ⊔ c) * (((b ⊔ a) ⊓ c) / (b ⊓ a ⊓ c))",
"pp... | [
"α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : MulLeftMono α\na b c : α\nthis : DistribLattice α := CommGroup.toDistribLattice α\n⊢ (b ⊔ c ⊔ (a ⊔ c)) / (b ⊓ a ⊔ c) * ((b ⊓ c ⊔ a ⊓ c) / (b ⊓ c ⊓ (a ⊓ c))) =\n (b ⊔ a ⊔ c) / (b ⊓ a ⊔ c) * (((b ⊔ a) ⊓ c) / (b ⊓ a ⊓ c))"
] | ← sup_inf_right, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Int.Parity | {
"line": 43,
"column": 2
} | {
"line": 43,
"column": 50
} | {
"line": 43,
"column": 51
} | [
{
"pp": "n : ℤ\n⊢ ∃ k, n = 2 * k ∨ n = 2 * k + 1",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"two_mul",
"_private.Mathlib.Algebra.Ring.Int.Parity.0.Int.even_or_odd'._simp_1_1",
"Exists",
"id",
"Distrib.t... | [
"n : ℤ\n⊢ (∃ x, n = x + x) ∨ ∃ x, n = x + x + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 64
} | {
"line": 210,
"column": 65
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Group α\ninst✝ : LinearOrder α\na b : α\nh : |a|ₘ = b\n⊢ a = b ∨ a = b⁻¹",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOne... | [
"α : Type u_1\ninst✝¹ : Group α\ninst✝ : LinearOrder α\na b : α\nh : |a|ₘ = b\n⊢ a = |a|ₘ ∨ a = |a|ₘ⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 215,
"column": 4
} | {
"line": 215,
"column": 79
} | {
"line": 215,
"column": 80
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝¹ : Group α\ninst✝ : LinearOrder α\nb : α\nh : |(|b|ₘ)|ₘ = |b|ₘ\n⊢ |b|ₘ = b ∨ |b|ₘ = b⁻¹",
"ppTerm": "?inl",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inl\nα : Type u_1\ninst✝¹ : Group α\ninst✝ : LinearOrder α\nb : α\nh : |(|b|ₘ)|ₘ = |b|ₘ\n⊢ |b|ₘ = b ∨ |b|ₘ = b⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 215,
"column": 4
} | {
"line": 215,
"column": 79
} | {
"line": 215,
"column": 80
} | [
{
"pp": "case inr\nα : Type u_1\ninst✝¹ : Group α\ninst✝ : LinearOrder α\nb : α\nh : ||b|ₘ⁻¹|ₘ = |b|ₘ\n⊢ |b|ₘ⁻¹ = b ∨ |b|ₘ⁻¹ = b⁻¹",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"InvolutiveInv.toInv",
"Gro... | [
"case inr\nα : Type u_1\ninst✝¹ : Group α\ninst✝ : LinearOrder α\nb : α\nh : ||b|ₘ⁻¹|ₘ = |b|ₘ\n⊢ |b|ₘ = b ∨ |b|ₘ = b⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 243,
"column": 4
} | {
"line": 243,
"column": 34
} | {
"line": 243,
"column": 35
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝² : Group α\ninst✝¹ : LinearOrder α\ninst✝ : MulLeftMono α\na : α\nh : 1 ≤ a\n⊢ |a|ₘ⁻¹ ≤ a",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"mabs_of_one_le",
"PartialOrd... | [
"case inl\nα : Type u_1\ninst✝² : Group α\ninst✝¹ : LinearOrder α\ninst✝ : MulLeftMono α\na : α\nh : 1 ≤ a\n⊢ a⁻¹ ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 249,
"column": 66
} | {
"line": 249,
"column": 77
} | {
"line": 249,
"column": 78
} | [
{
"pp": "α : Type u_1\ninst✝² : Group α\ninst✝¹ : LinearOrder α\ninst✝ : MulLeftMono α\na : α\n⊢ |a|ₘ⁻¹ ≤ a⁻¹",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Group α\ninst✝¹ : LinearOrder α\ninst✝ : MulLeftMono α\na : α\n⊢ |a|ₘ⁻¹ ≤ a⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 312,
"column": 29
} | {
"line": 312,
"column": 40
} | {
"line": 312,
"column": 41
} | [
{
"pp": "ι : Type u_2\nα : ι → Type u_3\ninst✝³ : (i : ι) → Group (α i)\nf : (i : ι) → α i\ninst✝² : (i : ι) → LinearOrder (α i)\ninst✝¹ : ∀ (i : ι), MulLeftMono (α i)\ninst✝ : ∀ (i : ι), MulRightMono (α i)\nh : |f|ₘ = 1\ni : ι\n⊢ f i = 1 i",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
... | [
"ι : Type u_2\nα : ι → Type u_3\ninst✝³ : (i : ι) → Group (α i)\nf : (i : ι) → α i\ninst✝² : (i : ι) → LinearOrder (α i)\ninst✝¹ : ∀ (i : ι), MulLeftMono (α i)\ninst✝ : ∀ (i : ι), MulRightMono (α i)\nh : |f|ₘ = 1\ni : ι\n⊢ f i = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Int | {
"line": 72,
"column": 20
} | {
"line": 72,
"column": 51
} | {
"line": 72,
"column": 52
} | [
{
"pp": "q n : ℕ\ndvd : gcd 0 q ∣ n\nle : pred 0 * q.pred ≤ n\nb : ℕ\neq : n = q * b\n⊢ 0 * 0 + b * q = n",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"... | [
"q n : ℕ\ndvd : gcd 0 q ∣ n\nle : pred 0 * q.pred ≤ n\nb : ℕ\neq : n = q * b\n⊢ n = q * b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Int | {
"line": 75,
"column": 20
} | {
"line": 75,
"column": 51
} | {
"line": 75,
"column": 52
} | [
{
"pp": "n p : ℕ\ndvd : (p + 1).gcd 0 ∣ n\nle : (p + 1).pred * pred 0 ≤ n\na : ℕ\neq : n = (p.gcd 0 + 1).gcd 0 * a\n⊢ a * (p + 1) + 0 * 0 = n",
"ppTerm": "?m.110",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"HMul.hMul",
"congrArg",
"AddMonoid... | [
"n p : ℕ\ndvd : (p + 1).gcd 0 ∣ n\nle : (p + 1).pred * pred 0 ≤ n\na : ℕ\neq : n = (p.gcd 0 + 1).gcd 0 * a\n⊢ n = a * (p + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.GCD | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 23
} | {
"line": 142,
"column": 24
} | [
{
"pp": "k n : ℕ\nhkn : n.Coprime k\nhk : 1 < k\n⊢ ∃ m, m < k ∧ n * m % k = 1",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"k n : ℕ\nhkn : n.Coprime k\nhk : 1 < k\n⊢ ∃ m, m < k ∧ n * m % k = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.GCD | {
"line": 253,
"column": 4
} | {
"line": 253,
"column": 54
} | {
"line": 253,
"column": 55
} | [
{
"pp": "case left\na b : ℤ\nha : a ≠ 0\n⊢ a.gcd b ∈ {n | 0 < n ∧ a.gcd b ∣ n}",
"ppTerm": "?left",
"assigned": true,
"usedConstants": [
"Int.gcd",
"Eq.mpr",
"Dvd.dvd",
"and_true",
"congrArg",
"Nat.instMonoid",
"setOf",
"Int.gcd_pos_iff._simp_1",
... | [
"case left\na b : ℤ\nha : a ≠ 0\n⊢ ¬a = 0 ∨ ¬b = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.GCD | {
"line": 273,
"column": 78
} | {
"line": 273,
"column": 93
} | {
"line": 273,
"column": 93
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : Monoid M\nn m : ℕ\ny : Mˣ\nhn : ↑(y ^ ↑n) = ↑1\nhm : ↑(y ^ ↑(m + 1)) = ↑1\n⊢ ↑(y ^ ↑((m + 1).gcd n)) = ↑1",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Nat.gcd",
"Units.val",
"Eq.mpr",
"Units.ext_iff",
"congrArg",
... | [
"case succ\nM : Type u_1\ninst✝ : Monoid M\nn m : ℕ\ny : Mˣ\nhn : y ^ ↑n = 1\nhm : y ^ ↑(m + 1) = 1\n⊢ y ^ ↑((m + 1).gcd n) = 1"
] | ← Units.ext_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.Int | {
"line": 93,
"column": 27
} | {
"line": 93,
"column": 69
} | {
"line": 93,
"column": 69
} | [
{
"pp": "n p q : ℕ\ndvd : ∃ x y, ↑n = ↑(p + 1) * x + ↑(q + 1) * y\nle : p * q ≤ n\na_n b_n : ℤ\neq : ↑n = ↑(p + 1) * a_n + ↑(q + 1) * b_n\na : ℤ := a_n % ↑q.succ\nb : ℤ := b_n + a_n / ↑q.succ * ↑p.succ\nthis : a * ↑p.succ + b * ↑q.succ = ↑n\nhb : b ≤ -1\nha : a_n % ↑q.succ < ↑(↑q.succ).natAbs\n⊢ ↑q * ↑p.succ + ... | [
"n p q : ℕ\ndvd : ∃ x y, ↑n = ↑(p + 1) * x + ↑(q + 1) * y\nle : p * q ≤ n\na_n b_n : ℤ\neq : ↑n = ↑(p + 1) * a_n + ↑(q + 1) * b_n\na : ℤ := a_n % ↑q.succ\nb : ℤ := b_n + a_n / ↑q.succ * ↑p.succ\nthis : a * ↑p.succ + b * ↑q.succ = ↑n\nhb : b ≤ -1\nha : a_n % ↑q.succ < ↑(↑q.succ).natAbs\n⊢ ↑p * ↑q + ↑q * 1 + (↑q * -1... | simp_rw [Nat.cast_succ, mul_add, mul_comm] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Algebra.Order.Monoid.Canonical.Defs | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 28
} | {
"line": 231,
"column": 29
} | [
{
"pp": "α : Type u\ninst✝² : Monoid α\ninst✝¹ : LinearOrder α\ninst✝ : CanonicallyOrderedMul α\na b c : α\n⊢ min (a * b) c = min (min a c * min b c) c",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"... | [
"α : Type u\ninst✝² : Monoid α\ninst✝¹ : LinearOrder α\ninst✝ : CanonicallyOrderedMul α\na b c : α\n⊢ min c (a * b) = min c (min c a * min c b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.GroupWithZero.Regular | {
"line": 50,
"column": 2
} | {
"line": 52,
"column": 15
} | {
"line": 54,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : MulZeroClass R\n⊢ ¬IsRightRegular 0 ↔ Nontrivial R",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Nontrivial",
"Eq.mpr",
"MulZeroClass.toMul",
"subsingleton_iff",
"congrArg",
... | [] | rw [nontrivial_iff, not_iff_comm, isRightRegular_zero_iff_subsingleton, subsingleton_iff]
push Not
exact Iff.rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.GroupWithZero.Regular | {
"line": 50,
"column": 2
} | {
"line": 52,
"column": 15
} | {
"line": 54,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : MulZeroClass R\n⊢ ¬IsRightRegular 0 ↔ Nontrivial R",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Nontrivial",
"Eq.mpr",
"MulZeroClass.toMul",
"subsingleton_iff",
"congrArg",
... | [] | rw [nontrivial_iff, not_iff_comm, isRightRegular_zero_iff_subsingleton, subsingleton_iff]
push Not
exact Iff.rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 13
} | {
"line": 66,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommMonoidWithTop α\na : α\nha : a ≠ ⊤\n⊢ IsAddRegular a",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝ : LinearOrderedAddCommMonoidWithTop α\na : α\nha : a ≠ ⊤\n⊢ IsAddRegular a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 149,
"column": 51
} | {
"line": 149,
"column": 73
} | {
"line": 151,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\na b : α\n⊢ a + b ≠ ⊤ ↔ a ≠ ⊤ ∧ b ≠ ⊤",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"instIsDedekindFiniteAddMonoid",
"Ne",
"IsAddU... | [] | simp [← isAddUnit_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 149,
"column": 51
} | {
"line": 149,
"column": 73
} | {
"line": 151,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\na b : α\n⊢ a + b ≠ ⊤ ↔ a ≠ ⊤ ∧ b ≠ ⊤",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"instIsDedekindFiniteAddMonoid",
"Ne",
"IsAddU... | [] | simp [← isAddUnit_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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