Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with
prim2 x0 x3,
prim2 x0 x1,
91630.. x0,
x1 = x3 leaving 3 subgoals.
The subproof is completed by applying L4.
Apply H5 with
λ x4 x5 . prim1 x1 x5.
The subproof is completed by applying unknownprop_70f06371245ce38fbbca963cb4d7e422ccf350d2e27735c617635b09cbcba701 with x0, x1.
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with
x1,
x0,
x3,
x1 = x3 leaving 3 subgoals.
The subproof is completed by applying L6.
Assume H7: x1 = x0.
Apply H5 with
λ x4 x5 . prim1 x3 x4.
The subproof is completed by applying unknownprop_70f06371245ce38fbbca963cb4d7e422ccf350d2e27735c617635b09cbcba701 with x0, x3.
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with
x3,
x0,
x1,
x1 = x3 leaving 3 subgoals.
The subproof is completed by applying L8.
Assume H9: x3 = x0.
Apply H9 with
λ x4 x5 . x1 = x5.
The subproof is completed by applying H7.
Assume H9: x3 = x1.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H9 with λ x5 x6 . x4 x6 x5.
Assume H7: x1 = x3.
The subproof is completed by applying H7.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H5 with λ x5 x6 . x4 x6 x5.
Apply unknownprop_af9539c7a0a0fd6f75a294ce5650975eaf393e80478d243f2a3f96e46b1a93a1 with
x0,
prim2 x0 x3,
x1 = x3 leaving 2 subgoals.
The subproof is completed by applying L6.
Assume H8:
∀ x4 . prim1 x4 (prim2 x0 x3) ⟶ x4 = x0.
Claim L9: x3 = x0
Apply H8 with
x3.
The subproof is completed by applying unknownprop_70f06371245ce38fbbca963cb4d7e422ccf350d2e27735c617635b09cbcba701 with x0, x3.
Apply L9 with
λ x4 x5 . x1 = x5.
Apply unknownprop_b3ea1d835e897a8898ececa703b067e0b342bf45a30307f3d93c658cb91e93a2 with
91630.. x0,
λ x4 x5 . prim1 (prim2 x0 x1) x5.
Apply unknownprop_b3ea1d835e897a8898ececa703b067e0b342bf45a30307f3d93c658cb91e93a2 with
x0,
λ x4 x5 . prim1 (prim2 x0 x1) (prim2 x5 (91630.. x0)).
Apply L10 with
λ x4 x5 . prim1 (prim2 x0 x1) x4.
The subproof is completed by applying unknownprop_893870ab8a49d622c10a8fe954eea30d7bd2b94aa27e9c6b21eab85a9f81d115 with
prim2 x0 x1,
91630.. x0.
Let x4 of type ι → ι → ο be given.
Apply unknownprop_30833a9978e304b25ffd59c347245315985872140acc9e441a97543a28184d79 with
91630.. x0,
prim2 x0 x1,
λ x5 x6 . x4 x6 x5.
The subproof is completed by applying L11.
Apply unknownprop_af9539c7a0a0fd6f75a294ce5650975eaf393e80478d243f2a3f96e46b1a93a1 with
x0,
prim2 x0 x1,
x1 = x0 leaving 2 subgoals.
The subproof is completed by applying L12.
Assume H14:
∀ x4 . prim1 x4 (prim2 x0 x1) ⟶ x4 = x0.
Apply H14 with
x1.
The subproof is completed by applying unknownprop_70f06371245ce38fbbca963cb4d7e422ccf350d2e27735c617635b09cbcba701 with x0, x1.