30 lines
787 B
Text
30 lines
787 B
Text
/-
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Copyright (c) 2015 Jeremy Avigad. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Jeremy Avigad
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The power function on the integers.
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-/
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import data.int.basic data.int.order data.int.div algebra.group_power data.nat.power
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namespace int
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open algebra
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definition int_has_pow_nat [reducible] [instance] [priority int.prio] : has_pow_nat int :=
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has_pow_nat.mk has_pow_nat.pow_nat
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/-
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definition nmul (n : ℕ) (a : ℤ) : ℤ := algebra.nmul n a
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infix [priority int.prio] ⬝ := nmul
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definition imul (i : ℤ) (a : ℤ) : ℤ := algebra.imul i a
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-/
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open nat
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theorem of_nat_pow (a n : ℕ) : of_nat (a^n) = (of_nat a)^n :=
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begin
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induction n with n ih,
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apply eq.refl,
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rewrite [pow_succ, pow_succ, of_nat_mul, ih]
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end
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end int
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