21 lines
477 B
Text
21 lines
477 B
Text
import data.nat
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open nat
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definition fact1 : nat → nat
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| 0 := 1
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| (succ a) := (succ a) * fact1 a
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open tactic
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example (a : nat) : fact1 a > 0 :=
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by do
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get_local "a" >>= λ H, induction_core semireducible H ("nat" <.> "rec_on") ["n", "iH"],
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trace_state, trace "-------",
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unfold ["fact1"],
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swap,
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unfold ["fact1"],
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trace_state,
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mk_const "mul_pos" >>= apply,
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mk_const ("nat" <.> "zero_lt_succ") >>= apply,
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assumption,
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mk_const "zero_lt_one" >>= apply
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