18 lines
691 B
Text
18 lines
691 B
Text
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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Leonardo de Moura
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import data.nat.order logic.wf
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open nat eq.ops
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theorem lt.wf [instance] : well_founded lt :=
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well_founded.intro
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(take n, nat.induction_on n
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(acc.intro zero (λ (y : nat) (H : y < 0),
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absurd H !not_lt_zero))
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(λ (n : nat) (iH : acc lt n),
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acc.intro (succ n) (λ (m : nat) (H : m < succ n),
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have H₁ : m < n ∨ m = n, from le_imp_lt_or_eq (succ_le_cancel (lt_imp_le_succ H)),
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or.elim H₁
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(assume Hlt : m < n, acc.inv iH Hlt)
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(assume Heq : m = n, Heq⁻¹ ▸ iH))))
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