30 lines
543 B
Text
30 lines
543 B
Text
|
example (p q : Prop) : p ∧ q ↔ q ∧ p :=
|
||
|
|
begin
|
||
|
|
apply iff.intro,
|
||
|
|
begin
|
||
|
|
intro H,
|
||
|
|
apply and.intro,
|
||
|
|
apply (and.elim_right H),
|
||
|
|
apply (and.elim_left H)
|
||
|
|
end,
|
||
|
|
begin
|
||
|
|
intro H,
|
||
|
|
apply and.intro,
|
||
|
|
apply (and.elim_right H),
|
||
|
|
apply (and.elim_left H)
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
example (p q : Prop) : p ∧ q ↔ q ∧ p :=
|
||
|
|
begin
|
||
|
|
apply iff.intro,
|
||
|
|
{intro H,
|
||
|
|
apply and.intro,
|
||
|
|
apply (and.elim_right H),
|
||
|
|
apply (and.elim_left H)},
|
||
|
|
{intro H,
|
||
|
|
apply and.intro,
|
||
|
|
apply (and.elim_right H),
|
||
|
|
apply (and.elim_left H)}
|
||
|
|
end
|