18 lines
No EOL
640 B
Text
18 lines
No EOL
640 B
Text
abbreviation Prop : Type.{1} := Type.{0}
|
|
variable and : Prop → Prop → Prop
|
|
infixl `∧`:25 := and
|
|
variable and_intro : forall (a b : Prop), a → b → a ∧ b
|
|
variables a b c d : Prop
|
|
axiom Ha : a
|
|
axiom Hb : b
|
|
axiom Hc : c
|
|
check
|
|
have a ∧ b, from and_intro a b Ha Hb,
|
|
have [fact] b ∧ a, from and_intro b a Hb Ha,
|
|
have H : a ∧ b, from and_intro a b Ha Hb,
|
|
have H [fact] : a ∧ b, from and_intro a b Ha Hb,
|
|
then have a ∧ b, from and_intro a b Ha Hb,
|
|
then have [fact] b ∧ a, from and_intro b a Hb Ha,
|
|
then have H : a ∧ b, from and_intro a b Ha Hb,
|
|
then have H [fact] : a ∧ b, from and_intro a b Ha Hb,
|
|
Ha |