lean2/tests/lean/run/have6.lean
2014-09-19 15:54:32 -07:00

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651 B
Text

definition 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 [visible] b ∧ a, from and_intro b a Hb Ha,
have H : a ∧ b, from and_intro a b Ha Hb,
have H [visible] : a ∧ b, from and_intro a b Ha Hb,
then have a ∧ b, from and_intro a b Ha Hb,
then have [visible] b ∧ a, from and_intro b a Hb Ha,
then have H : a ∧ b, from and_intro a b Ha Hb,
then have H [visible] : a ∧ b, from and_intro a b Ha Hb,
Ha