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d03762b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | /- 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
|