33 lines
1,008 B
Text
33 lines
1,008 B
Text
/-
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Copyright (c) 2015 Floris van Doorn. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Module: hit.cylinder
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Authors: Floris van Doorn
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Mapping cylinders
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-/
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/- The hit mapping cylinder is primitive, declared in init.hit. -/
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open eq
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namespace cylinder
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variables {A B : Type} {f : A → B}
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protected definition elim {P : Type} (Pbase : B → P) (Ptop : A → P)
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(Pseg : Π(a : A), Ptop a = Pbase (f a)) {b : B} (x : cylinder f b) : P :=
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cylinder.rec Pbase Ptop (λa, !tr_constant ⬝ Pseg a) x
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protected definition elim_on [reducible] {P : Type} {b : B} (x : cylinder f b)
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(Pbase : B → P) (Ptop : A → P)
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(Pseg : Π(a : A), Ptop a = Pbase (f a)) : P :=
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cylinder.elim Pbase Ptop Pseg x
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definition elim_seg {P : Type} (Pbase : B → P) (Ptop : A → P)
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(Pseg : Π(a : A), Ptop a = Pbase (f a)) {b : B} (x : cylinder f b) (a : A) :
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ap (elim Pbase Ptop Pseg) (seg f a) = sorry ⬝ Pseg a ⬝ sorry :=
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sorry
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end cylinder
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