49 lines
1.5 KiB
Text
49 lines
1.5 KiB
Text
constant f : nat → nat
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constant p : nat → Prop
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/- The following axiom produces a matching loop -/
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axiom fax : ∀ x, f (: f x :) = nat.succ x
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axiom px : ∀ x, p x
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attribute [ematch] fax
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set_option trace.smt.ematch true
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lemma ex1 (a b c : nat) : f a = b → p a :=
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begin [smt]
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intros, iterate {ematch},
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ematch_using [px]
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end
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constant r : nat → nat → Prop
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axiom rtrans : ∀ a b c, r a b → r b c → r a c
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attribute [ematch] rtrans
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example (a1 a2 a3 a4 a5 a6 a7 a8 : nat) :
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r a1 a2 → r a2 a3 → r a3 a4 → r a4 a5 → r a5 a6 → r a6 a7 → r a7 a8 → r a1 a8 ∨ p 0 :=
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begin [smt] with {em_cfg := {max_generation := 2}},
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intros,
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eblast, -- fails to prove because max_generation is too low
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ematch_using [px]
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end
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example (a1 a2 a3 a4 a5 a6 a7 a8 : nat) :
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r a1 a2 → r a2 a3 → r a3 a4 → r a4 a5 → r a5 a6 → r a6 a7 → r a7 a8 → r a1 a8 :=
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begin [smt] with {em_cfg := {max_generation := 10}},
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intros,
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eblast -- succeeds
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end
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attribute [ematch] list.map
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example (f : nat → nat) (l : list nat) : l = [1, 2, 3, 4, 5, 6, 7, 8, 9] → list.map f l = [f 1, f 2, f 3, f 4, f 5, f 6, f 7, f 8, f 9] ∨ p 0 :=
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begin [smt] with {em_cfg := {max_generation := 5}},
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intros,
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eblast, -- fails to prove because max_generation is too low
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ematch_using [px]
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end
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example (f : nat → nat) (l : list nat) : l = [1, 2, 3, 4, 5, 6, 7, 8, 9] → list.map f l = [f 1, f 2, f 3, f 4, f 5, f 6, f 7, f 8, f 9] :=
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begin [smt] with {em_cfg := {max_generation := 10}},
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intros,
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eblast -- succeeds
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end
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