33 lines
712 B
Text
33 lines
712 B
Text
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import algebra.function
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import logic.funext
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open function
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structure bijection (A : Type) :=
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(func finv : A → A)
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(linv : finv ∘ func = id)
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(rinv : func ∘ finv = id)
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attribute bijection.func [coercion]
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namespace bijection
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variable {A : Type}
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protected theorem eq {f g : bijection A}
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(func_eq : func f = func g) (finv_eq : finv f = finv g) : f = g :=
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begin
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revert finv_eq,
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revert func_eq,
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cases g with [gfunc, gfinv, glinv, grinv],
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cases f with [func, finv, linv, rinv],
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state,
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esimp,
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intros [func_eq, finv_eq],
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revert grinv, revert glinv, revert rinv, revert linv,
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rewrite [func_eq, finv_eq],
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intros [H1, H2, H3, H4],
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apply rfl
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end
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end bijection
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