lean2/tests/lean/hott/constr_tac.hlean
2015-12-09 12:36:11 -08:00

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open prod
example (a b c : Type) : a → b → c → a × b × c :=
begin
intro Ha Hb Hc,
repeat (split | assumption)
end
example (a b : Type) : a → sum a b :=
begin
intro Ha,
left,
assumption
end
example (a b : Type) : b → sum a b :=
begin
intro Ha,
right,
assumption
end
open nat
example (a : nat) : a > 0 → Σ(x : ), x > 0 :=
begin
intro Ha,
existsi a,
apply Ha
end
example : nat :=
begin
constructor 1
end
example : nat :=
begin
constructor 2,
constructor 2,
constructor 1
end