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