Let x0 of type ι be given.
Apply unknownprop_99b6e78091df4beabbcffd047e78b6c42c4c5c9619b88f6d54bab1d1943a087f with
x0,
45abd.. x0 leaving 3 subgoals.
Apply unknownprop_4e1e69c1892e0ea60ddce505f4abc22cbcb234a9739664b13e3a31f3eaeef30f with
x0,
λ x1 x2 . prim1 (e4431.. x0) x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying unknownprop_38ce50d6b52a0a920b530e7796207ec902a42d65414467df1ecd3efb123f4cb9 with
e4431.. x0.
Apply SNoEq_sym_ with
e4431.. x0,
45abd.. x0,
x0.
Apply unknownprop_a7690d464378e6bcdfaef0c9e813d4ef5fa31adb6bb3047eb361bc612b21cd85 with
x0.
The subproof is completed by applying H0.
Apply unknownprop_fd9b40eb539c66a16aeafdf7cb0dd693c0d7c9a58e3fa4d863eaa20d4568f5a7 with
x0.
The subproof is completed by applying H0.