Let x0 of type ι → ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_219a5692ece616b4a88502d80a85b644180cde982b21251f92a23d11d1a5d022 with
Repl (UPair x1 x2) (λ x3 . x0 x3),
UPair (x0 x1) (x0 x2) leaving 2 subgoals.
Let x3 of type ι be given.
Apply unknownprop_89e422bb3b8a01dd209d7f2f210df650a435fc3e6005e0f59c57a5e7a59a6d0e with
UPair x1 x2,
x0,
x3,
In x3 (UPair (x0 x1) (x0 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x4 of type ι be given.
Assume H2: x3 = x0 x4.
Apply H2 with
λ x5 x6 . In x6 (UPair (x0 x1) (x0 x2)).
Apply unknownprop_75ddf832b1631756e4bbf96a65e15fca654982aa51c8799a97b68da7b8a2da12 with
x4,
x1,
x2,
In (x0 x4) (UPair (x0 x1) (x0 x2)) leaving 3 subgoals.
The subproof is completed by applying H1.
Assume H3: x4 = x1.
Apply H3 with
λ x5 x6 . In (x0 x6) (UPair (x0 x1) (x0 x2)).
The subproof is completed by applying unknownprop_f40d13744d00ec34b223eab4c005556ef718e0ee3d9e509403edfd952d571ca0 with x0 x1, x0 x2.
Assume H3: x4 = x2.
Apply H3 with
λ x5 x6 . In (x0 x6) (UPair (x0 x1) (x0 x2)).
The subproof is completed by applying unknownprop_062c64c10c58e9562a87a79165ec64b8525d3f91b15ae8561687c786947b4cb0 with x0 x1, x0 x2.
Let x3 of type ι be given.
Assume H0:
In x3 (UPair (x0 x1) (x0 x2)).
Apply unknownprop_75ddf832b1631756e4bbf96a65e15fca654982aa51c8799a97b68da7b8a2da12 with
x3,
x0 x1,
x0 x2,
In x3 (Repl (UPair x1 x2) (λ x4 . x0 x4)) leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x3 = x0 x1.
Apply H1 with
λ x4 x5 . In x5 (Repl (UPair x1 x2) (λ x6 . x0 x6)).
Apply unknownprop_63c308b92260dbfca8c9530846e6836ba3e6be221cc8e80fd61db913e01bdacf with
UPair x1 x2,
x0,
x1.
The subproof is completed by applying unknownprop_f40d13744d00ec34b223eab4c005556ef718e0ee3d9e509403edfd952d571ca0 with x1, x2.
Assume H1: x3 = x0 x2.
Apply H1 with
λ x4 x5 . In x5 (Repl (UPair x1 x2) (λ x6 . x0 x6)).
Apply unknownprop_63c308b92260dbfca8c9530846e6836ba3e6be221cc8e80fd61db913e01bdacf with
UPair x1 x2,
x0,
x2.
The subproof is completed by applying unknownprop_062c64c10c58e9562a87a79165ec64b8525d3f91b15ae8561687c786947b4cb0 with x1, x2.