Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Apply unknownprop_4b13af0994345cb2bf2bb7ad85bc935012652f874cfc879eb5167bd6f7e5286b with
da24e.. x0 x2 x4,
x1,
x3,
x5.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x6 x7 . x0 = x7.
The subproof is completed by applying unknownprop_d5c666295286bdabbe3b4b402072fcffded5f890a3391136bdff5cc6214a1e24 with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 . prim1 x6 x0 ⟶ x2 x6 = x3 x6,
∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι be given.
Apply unknownprop_4f3afbbe58bbb9a1658cfb089e3b5326b7bc654d1513ffdbae5a0e4dfeed0a85 with
x0,
x2,
x4,
x6,
λ x7 x8 . x8 = x3 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . f482f.. (f482f.. x8 (4ae4a.. 4a7ef..)) x6 = x3 x6.
Let x7 of type ι → ι → ο be given.
Apply unknownprop_4f3afbbe58bbb9a1658cfb089e3b5326b7bc654d1513ffdbae5a0e4dfeed0a85 with
x1,
x3,
x5,
x6,
λ x8 x9 . x7 x9 x8.
The subproof is completed by applying L4.
Let x6 of type ι be given.
Apply unknownprop_aa3a1ba9e3b66a6d45c93924e38055beb531cb5ca109751b2117af33661559ee with
x0,
x2,
x4,
x6,
λ x7 x8 : ο . x8 = x5 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . decode_p (f482f.. x8 (4ae4a.. (4ae4a.. 4a7ef..))) x6 = x5 x6.
Let x7 of type ο → ο → ο be given.
Apply unknownprop_aa3a1ba9e3b66a6d45c93924e38055beb531cb5ca109751b2117af33661559ee with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.