lean2/tests/lean/interactive/t12.lean

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(*
import("tactic.lua")
-- Define a simple tactic using Lua
auto = Repeat(OrElse(assumption_tac(), conj_tac(), conj_hyp_tac()))
*)
theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := (by auto),
lemma2 : B := (by auto)
in (show B /\ A, by auto)
print environment 1. -- print proof for the previous theorem
theorem T2 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := _,
lemma2 : B := _
in _.
auto. done.
auto. done.
auto. done.
theorem T3 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := _,
lemma2 : B := _
in _.
conj_hyp. exact. done.
conj_hyp. exact. done.
apply and_intro. exact. done.
theorem T4 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := _,
lemma2 : B := _
in (show B /\ A, by auto).
conj_hyp. exact. done.
conj_hyp. exact. done.