Let x0 of type ο be given.
Apply orIL with
4a7ef.. = 4a7ef..,
x0.
Let x1 of type ι → ι → ο be given.
The subproof is completed by applying H0.
Apply Eps_i_ax with
λ x1 . or (x1 = 4a7ef..) x0,
4a7ef...
The subproof is completed by applying L0.
Apply orIL with
not (91630.. 4a7ef.. = 4a7ef..),
x0.
Apply unknownprop_da3368fefc81e401e6446c98c0c04ab87d76d6f97c47fe5fd07c1e3c2f00ef6a with
4a7ef...
Apply H2 with
λ x1 x2 . prim1 4a7ef.. x1.
The subproof is completed by applying unknownprop_c6d721b795faf1c324094ad380dfe62a3a5dc2ef0b2edf42237be188f6768728 with
4a7ef...
Apply L1 with
or x0 (not x0) leaving 2 subgoals.
Apply L3 with
or x0 (not x0) leaving 2 subgoals.
Apply orIR with
x0,
not x0.
Assume H6: x0.
Apply pred_ext with
λ x1 . or (x1 = 4a7ef..) x0,
λ x1 . or (not (x1 = 4a7ef..)) x0.
Let x1 of type ι be given.
Apply iffI with
(λ x2 . or (x2 = 4a7ef..) x0) x1,
(λ x2 . or (not (x2 = 4a7ef..)) x0) x1 leaving 2 subgoals.
Apply orIR with
not (x1 = 4a7ef..),
x0.
The subproof is completed by applying H6.
Apply orIR with
x1 = 4a7ef..,
x0.
The subproof is completed by applying H6.
Apply H5.
Apply L7 with
λ x1 x2 : ι → ο . prim0 x1 = 4a7ef...
The subproof is completed by applying H4.
Assume H5: x0.
Apply orIL with
x0,
not x0.
The subproof is completed by applying H5.
Assume H4: x0.
Apply orIL with
x0,
not x0.
The subproof is completed by applying H4.