46db59d1d9
Remark: when splitting an `if-then-else` term, the subgoals now have tags `isTrue` and `isFalse` instead of `inl` and `inr`. closes #4313 --------- Co-authored-by: Mario Carneiro <di.gama@gmail.com>
27 lines
772 B
Text
27 lines
772 B
Text
example {A B : Prop} {p : Prop} [Decidable p] (h : if p then A else B) :
|
||
A ∨ B := by
|
||
split at h
|
||
· exact .inl h
|
||
· exact .inr h
|
||
|
||
example {A B : Type} {p : Prop} [Decidable p] (h : if p then A else B) :
|
||
Sum A B := by
|
||
split at h
|
||
· exact .inl h
|
||
· exact .inr h
|
||
|
||
example {A B : Type} (h : match b with | true => A | false => B) :
|
||
Sum A B := by
|
||
split at h
|
||
· exact .inl h
|
||
· exact .inr h
|
||
|
||
open Int in
|
||
theorem bmod_add_bmod_congr : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n := by
|
||
rw [bmod_def x n]
|
||
split -- `split` now generates the more meaningful `isTrue` and `isFalse` tags.
|
||
case isTrue p =>
|
||
simp only [emod_add_bmod_congr]
|
||
case isFalse p =>
|
||
rw [Int.sub_eq_add_neg, Int.add_right_comm, ←Int.sub_eq_add_neg]
|
||
simp
|