2015-05-27 23:38:31 +00:00
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/-
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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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Cubeovers
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-/
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import .squareover .cube
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open equiv is_equiv
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namespace eq
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-- we need to specify B explicitly, also in pathovers
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inductive cubeover {A : Type} (B : A → Type) {a₀₀₀ : A} {b₀₀₀ : B a₀₀₀}
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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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{s₀₁₁ : square p₀₁₀ p₀₁₂ p₀₀₁ p₀₂₁}
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{s₂₁₁ : square p₂₁₀ p₂₁₂ p₂₀₁ p₂₂₁}
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2015-07-29 12:17:16 +00:00
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{s₁₀₁ : square p₁₀₀ p₁₀₂ p₀₀₁ p₂₀₁}
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{s₁₂₁ : square p₁₂₀ p₁₂₂ p₀₂₁ p₂₂₁}
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2015-11-24 21:44:42 +00:00
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(c : cube s₀₁₁ s₂₁₁ s₁₀₁ s₁₂₁ s₁₁₀ s₁₁₂)
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2015-05-27 23:38:31 +00:00
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{b₀₂₀ : B a₀₂₀} {b₂₀₀ : B a₂₀₀} {b₂₂₀ : B a₂₂₀}
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{b₀₀₂ : B a₀₀₂} {b₀₂₂ : B a₀₂₂} {b₂₀₂ : B a₂₀₂} {b₂₂₂ : B a₂₂₂}
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{q₁₀₀ : pathover B b₀₀₀ p₁₀₀ b₂₀₀} {q₀₁₀ : pathover B b₀₀₀ p₀₁₀ b₀₂₀}
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{q₀₀₁ : pathover B b₀₀₀ p₀₀₁ b₀₀₂} {q₁₂₀ : pathover B b₀₂₀ p₁₂₀ b₂₂₀}
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{q₂₁₀ : pathover B b₂₀₀ p₂₁₀ b₂₂₀} {q₂₀₁ : pathover B b₂₀₀ p₂₀₁ b₂₀₂}
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{q₁₀₂ : pathover B b₀₀₂ p₁₀₂ b₂₀₂} {q₀₁₂ : pathover B b₀₀₂ p₀₁₂ b₀₂₂}
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{q₀₂₁ : pathover B b₀₂₀ p₀₂₁ b₀₂₂} {q₁₂₂ : pathover B b₀₂₂ p₁₂₂ b₂₂₂}
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{q₂₁₂ : pathover B b₂₀₂ p₂₁₂ b₂₂₂} {q₂₂₁ : pathover B b₂₂₀ p₂₂₁ b₂₂₂}
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(t₀₁₁ : squareover B s₀₁₁ q₀₁₀ q₀₁₂ q₀₀₁ q₀₂₁)
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2015-07-29 12:17:16 +00:00
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(t₂₁₁ : squareover B s₂₁₁ q₂₁₀ q₂₁₂ q₂₀₁ q₂₂₁)
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(t₁₀₁ : squareover B s₁₀₁ q₁₀₀ q₁₀₂ q₀₀₁ q₂₀₁)
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2015-11-24 21:44:42 +00:00
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(t₁₂₁ : squareover B s₁₂₁ q₁₂₀ q₁₂₂ q₀₂₁ q₂₂₁)
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(t₁₁₀ : squareover B s₁₁₀ q₀₁₀ q₂₁₀ q₁₀₀ q₁₂₀)
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(t₁₁₂ : squareover B s₁₁₂ q₀₁₂ q₂₁₂ q₁₀₂ q₁₂₂), Type :=
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2015-05-27 23:38:31 +00:00
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idcubeo : cubeover B idc idso idso idso idso idso idso
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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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end eq
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