43 lines
1.1 KiB
Text
43 lines
1.1 KiB
Text
-- 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 logic
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namespace bit
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inductive bit : Type :=
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| b0 : bit
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| b1 : bit
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notation `'0` := b0
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notation `'1` := b1
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theorem inhabited_bit [instance] : inhabited bit
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:= inhabited_intro b0
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definition cond {A : Type} (b : bit) (t e : A)
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:= bit_rec e t b
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theorem cond_b0 {A : Type} (t e : A) : cond b0 t e = e
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:= refl (cond b0 t e)
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theorem cond_b1 {A : Type} (t e : A) : cond b1 t e = t
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:= refl (cond b1 t e)
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definition bor (a b : bit)
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:= bit_rec (bit_rec b0 b1 b) b1 a
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section
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-- create section for setting temporary configuration option
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set_option unifier.unfold_opaque true
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theorem bor_b1_left (a : bit) : bor b1 a = b1
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:= refl (bor b1 a)
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theorem bor_b1_right (a : bit) : bor a b1 = b1
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:= bit_rec (refl (bor b0 b1)) (refl (bor b1 b1)) a
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theorem bor_b0_left (a : bit) : bor b0 a = a
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:= bit_rec (refl (bor b0 b0)) (refl (bor b0 b1)) a
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theorem bor_b0_right (a : bit) : bor a b0 = a
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:= bit_rec (refl (bor b0 b0)) (refl (bor b1 b0)) a
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end
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end
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