Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι be given.
Assume H0:
∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3.
Apply set_ext with
0fc90.. x0 (λ x3 . x1 x3),
0fc90.. x0 (λ x3 . x2 x3) leaving 2 subgoals.
Apply unknownprop_08b94e577f2cbe6835cdccba6475d924b6ff6b40ecbbb0ed11454f064a913a35 with
x0,
x1,
x2.
The subproof is completed by applying H0.
Apply unknownprop_08b94e577f2cbe6835cdccba6475d924b6ff6b40ecbbb0ed11454f064a913a35 with
x0,
x2,
x1.
Let x3 of type ι be given.
Let x4 of type ι → ι → ο be given.
Apply H0 with
x3,
λ x5 x6 . x4 x6 x5.
The subproof is completed by applying H1.