| /- Copyright (c) Heather Macbeth, 2023. All rights reserved. -/ |
| import Mathlib.Data.Prod.Basic |
| import Mathlib.Tactic.Replace |
|
|
| open Lean |
|
|
| theorem Prod.congr {a1 a2 : A} {b1 b2 : B} (h : a1 = a2 ∧ b1 = b2) : (a1, b1) = (a2, b2) := |
| Iff.mpr Prod.mk.inj_iff h |
|
|
| theorem Prod.inj {a1 a2 : A} {b1 b2 : B} (h : (a1, b1) = (a2, b2)) : a1 = a2 ∧ b1 = b2 := |
| Iff.mp Prod.mk.inj_iff h |
|
|
| theorem Prod.inj2 {a1 a2 : A} {b1 b2 : B} {c1 c2 : C} (h : (a1, b1, c1) = (a2, b2, c2)) : |
| a1 = a2 ∧ b1 = b2 ∧ c1 = c2 := |
| let h' := Prod.inj h |
| ⟨h'.1, Prod.inj h'.2⟩ |
|
|
| macro_rules | `(tactic| constructor) => `(tactic| refine Prod.congr (And.intro ?_ ?_)) |
|
|
| -- example (h : x = 1) : (x, 3) = (1, 3) := by |
| -- constructor |
|
|
| macro_rules |
| | `(tactic| obtain $pat? $[ : $ty]? := $val) => |
| if Syntax.isIdent val then |
| let h := val.raw.getId |
| `(tactic| |
| replace $(mkIdent h):ident := Prod.inj $(mkIdent h):ident ; |
| obtain $pat? $[ : $ty]? := $val) |
| else |
| `(tactic| have h := Prod.inj $val ; obtain $pat? $[ : $ty]? := h) |
|
|
| macro_rules |
| | `(tactic| obtain $pat? $[ : $ty]? := $val) => |
| if Syntax.isIdent val then |
| let h := val.raw.getId |
| `(tactic| |
| replace $(mkIdent h):ident := Prod.inj2 $(mkIdent h):ident ; |
| obtain $pat? $[ : $ty]? := $val) |
| else |
| `(tactic| have h := Prod.inj2 $val ; obtain $pat? $[ : $ty]? := h) |
|
|
|
|
| -- example (h : (x, 3) = (1, 3)) : False := by |
| -- obtain ⟨h1, h2⟩ := h |
|
|
| -- example (h : (x, 3) = (1, 3) ∨ y = 2) (h' : (3, 4) = (z, w)): False := by |
| -- obtain h1 | h2 := h |
|
|
| -- example (h : ∀ x, (x, 3) = (1, 3)) : False := by |
| -- obtain ⟨h1, h2⟩ := h 2 |
|
|
| -- example (h : ∀ x, (x, 3) = (1, 3) ∨ 4 = 3) : False := by |
| -- obtain h1 | h2 := h 2 |
|
|
