48 lines
2.8 KiB
Text
48 lines
2.8 KiB
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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Author: Floris van Doorn
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Cubes
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-/
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import .square
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open equiv is_equiv
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namespace eq
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inductive cube {A : Type} {a₀₀₀ : A}
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: Π{a₂₀₀ a₀₂₀ a₂₂₀ a₀₀₂ a₂₀₂ a₀₂₂ a₂₂₂ : A}
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{p₁₀₀ : a₀₀₀ = a₂₀₀} {p₀₁₀ : a₀₀₀ = a₀₂₀} {p₀₀₁ : a₀₀₀ = a₀₀₂}
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{p₁₂₀ : a₀₂₀ = a₂₂₀} {p₂₁₀ : a₂₀₀ = a₂₂₀} {p₂₀₁ : a₂₀₀ = a₂₀₂}
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{p₁₀₂ : a₀₀₂ = a₂₀₂} {p₀₁₂ : a₀₀₂ = a₀₂₂} {p₀₂₁ : a₀₂₀ = a₀₂₂}
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{p₁₂₂ : a₀₂₂ = a₂₂₂} {p₂₁₂ : a₂₀₂ = a₂₂₂} {p₂₂₁ : a₂₂₀ = a₂₂₂}
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(s₁₁₀ : square p₀₁₀ p₂₁₀ p₁₀₀ p₁₂₀)
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(s₁₁₂ : square p₀₁₂ p₂₁₂ p₁₀₂ p₁₂₂)
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(s₁₀₁ : square p₁₀₀ p₁₀₂ p₀₀₁ p₂₀₁)
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(s₁₂₁ : square p₁₂₀ p₁₂₂ p₀₂₁ p₂₂₁)
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(s₀₁₁ : square p₀₁₀ p₀₁₂ p₀₀₁ p₀₂₁)
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(s₂₁₁ : square p₂₁₀ p₂₁₂ p₂₀₁ p₂₂₁), Type :=
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idc : cube ids ids ids ids ids ids
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variables {A : Type} {a₀₀₀ a₂₀₀ a₀₂₀ a₂₂₀ a₀₀₂ a₂₀₂ a₀₂₂ a₂₂₂ : A}
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{p₁₀₀ : a₀₀₀ = a₂₀₀} {p₀₁₀ : a₀₀₀ = a₀₂₀} {p₀₀₁ : a₀₀₀ = a₀₀₂}
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{p₁₂₀ : a₀₂₀ = a₂₂₀} {p₂₁₀ : a₂₀₀ = a₂₂₀} {p₂₀₁ : a₂₀₀ = a₂₀₂}
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{p₁₀₂ : a₀₀₂ = a₂₀₂} {p₀₁₂ : a₀₀₂ = a₀₂₂} {p₀₂₁ : a₀₂₀ = a₀₂₂}
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{p₁₂₂ : a₀₂₂ = a₂₂₂} {p₂₁₂ : a₂₀₂ = a₂₂₂} {p₂₂₁ : a₂₂₀ = a₂₂₂}
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{s₁₁₀ : square p₀₁₀ p₂₁₀ p₁₀₀ p₁₂₀}
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{s₁₁₂ : square p₀₁₂ p₂₁₂ p₁₀₂ p₁₂₂}
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{s₁₀₁ : square p₁₀₀ p₁₀₂ p₀₀₁ p₂₀₁}
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{s₁₂₁ : square p₁₂₀ p₁₂₂ p₀₂₁ p₂₂₁}
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{s₀₁₁ : square p₀₁₀ p₀₁₂ p₀₀₁ p₀₂₁}
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{s₂₁₁ : square p₂₁₀ p₂₁₂ p₂₀₁ p₂₂₁}
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definition idc [reducible] [constructor] := @cube.idc
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definition idcube [reducible] [constructor] (a : A) := @cube.idc A a
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definition rfl1 : cube s₁₁₀ s₁₁₀ vrfl vrfl vrfl vrfl := by induction s₁₁₀; exact idc
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definition rfl2 : cube hrfl hrfl s₁₀₁ s₁₀₁ hrfl hrfl := by induction s₁₀₁; exact idc
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definition rfl3 : cube vrfl vrfl hrfl hrfl s₁₁₀ s₁₁₀ := by induction s₁₁₀; exact idc
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end eq
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