Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x4 of type ι → ο be given.
Apply unknownprop_4be0565ac5b41f138f7a30d0a9f34a5d126bb341d2eeaa545aa7f0c1552b9722 with
add_CSNo x1 x2,
y3,
λ x5 . x4 leaving 3 subgoals.
Apply CSNo_add_CSNo with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_1a3b6d576749bdb66b853eab2e35cc4332be69b97fdfebcc7e17a4a552a3d204 with
y3,
x1,
x2,
λ x5 . x4 leaving 4 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x6 of type ι → ο be given.
Apply unknownprop_4be0565ac5b41f138f7a30d0a9f34a5d126bb341d2eeaa545aa7f0c1552b9722 with
x4,
x2,
λ x7 x8 . (λ x9 . x6) (add_CSNo x7 (mul_CSNo x4 y3)) (add_CSNo x8 (mul_CSNo x4 y3)) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H0.
Apply unknownprop_4be0565ac5b41f138f7a30d0a9f34a5d126bb341d2eeaa545aa7f0c1552b9722 with
x4,
y3,
λ x7 x8 . (λ x9 . x6) (add_CSNo (mul_CSNo x2 x4) x7) (add_CSNo (mul_CSNo x2 x4) x8) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
set y6 to be λ x6 . y5
Apply L4 with
λ x7 . y6 x7 y5 ⟶ y6 y5 x7 leaving 2 subgoals.
Assume H5: y6 y5 y5.
The subproof is completed by applying H5.
The subproof is completed by applying L4.
Let x4 of type ι → ι → ο be given.
Apply L3 with
λ x5 . x4 x5 y3 ⟶ x4 y3 x5.
Assume H4: x4 y3 y3.
The subproof is completed by applying H4.