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