25 lines
1.9 KiB
Text
25 lines
1.9 KiB
Text
lift.equations._eqn_1 : ∀ {m k : ℕ} (f : fi m → fi k) (v : fi (m + 0)), @lift m k f 0 v = f v
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lift.equations._eqn_2 : ∀ {m k : ℕ} (f : fi m → fi k) (n : ℕ), @lift m k f (succ n) (@f0 (m + n)) = @f0 (k + n)
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lift.equations._eqn_3 :
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∀ {m k : ℕ} (f : fi m → fi k) (n : ℕ) (i : fi (m + n)),
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@lift m k f (succ n) (@fs (m + n) i) = @fs (k + n) (@lift m k f n i)
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to_nat.equations._eqn_1 : ∀ (n : ℕ), @to_nat (succ n) (@f0 n) = 0
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to_nat.equations._eqn_2 : ∀ (n : ℕ) (i : fi n), @to_nat (succ n) (@fs n i) = succ (@to_nat n i)
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inject.equations._eqn_1 : ∀ (n : ℕ) (i : fi n), @inject (succ n) (@fs n i) (@f0 (@to_nat n i)) = @f0 n
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inject.equations._eqn_2 :
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∀ (n : ℕ) (i : fi n) (j : fi (@to_nat n i)),
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@inject (succ n) (@fs n i) (@fs (@to_nat n i) j) = @fs n (@inject n i j)
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inject'.equations._eqn_1 : ∀ (n : ℕ) (i : fi n), @inject' (succ n) (@fs n i) (@f0 (@to_nat n i)) = @f0 n
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inject'.equations._eqn_2 :
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∀ (n : ℕ) (i : fi n) (j : fi (@to_nat n i)),
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@inject' (succ n) (@fs n i) (@fs (@to_nat n i) j) = @fs n (@inject' n i j)
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raise.equations._eqn_1 : ∀ {m : ℕ} (i : fi m), @raise m 0 i = i
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raise.equations._eqn_2 : ∀ {m : ℕ} (n : ℕ) (i : fi m), @raise m (succ n) i = @fs (m + n) (@raise m n i)
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deg.equations._eqn_1 : ∀ (n : ℕ) (j : fi (succ n)), @deg (succ n) (@f0 (succ n)) j = @fs (succ n) j
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deg.equations._eqn_2 : ∀ (n : ℕ) (i : fi (succ n)), @deg (succ n) (@fs (succ n) i) (@f0 n) = @f0 (succ n)
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deg.equations._eqn_3 :
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∀ (n : ℕ) (i : fi (succ n)) (j : fi n), @deg (succ n) (@fs (succ n) i) (@fs n j) = @fs (succ n) (@deg n i j)
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deg'.equations._eqn_1 : ∀ (n : ℕ) (j : fi (succ n)), @deg' (succ n) (@f0 (succ n)) j = @fs (succ n) j
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deg'.equations._eqn_2 : ∀ (n : ℕ) (i : fi (succ n)), @deg' (succ n) (@fs (succ n) i) (@f0 n) = @f0 (succ n)
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deg'.equations._eqn_3 :
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∀ (n : ℕ) (i : fi (succ n)) (j : fi n), @deg' (succ n) (@fs (succ n) i) (@fs n j) = @fs (succ n) (@deg' n i j)
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