Let x0 of type ι be given.
Let x1 of type ι be given.
Claim L2: ∀ x4 : ι → ο . x4 y3 ⟶ x4 y2
Let x4 of type ι → ο be given.
Apply unknownprop_cce65446ff59911a5cd0f0aa52c7a372f2f1990c39bd3db3c9fd2ea818c2e216 with
y2,
λ x5 x6 . bc82c.. y2 y3 = bc82c.. x6 (ce322.. y3),
λ x5 . x4 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_cce65446ff59911a5cd0f0aa52c7a372f2f1990c39bd3db3c9fd2ea818c2e216 with
y3,
λ x5 x6 . bc82c.. y2 y3 = bc82c.. y2 x6 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H3.
set y5 to be λ x5 . x4
Apply unknownprop_8caab58746e5d2d24e79c56b1fd1ad38271bed0128653f24088edadc36aa9114 with
bc82c.. (ce322.. y2) (ce322.. y3),
λ x6 x7 . y5 x7 x6.
Claim L3: ∀ x8 : ι → ο . x8 y7 ⟶ x8 y6
Let x8 of type ι → ο be given.
set y9 to be λ x9 . x8
Apply unknownprop_a7cae15d14a6e4791f91b3ea7ac5511c0d8df820499a97872d4161ec0acb2004 with
y5,
λ x10 x11 . 4a7ef.. = bc82c.. x11 (f6a32.. y6),
λ x10 x11 . y9 (236dc.. (bc82c.. (ce322.. y5) (ce322.. y6)) x10) (236dc.. (bc82c.. (ce322.. y5) (ce322.. y6)) x11) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_a7cae15d14a6e4791f91b3ea7ac5511c0d8df820499a97872d4161ec0acb2004 with
y6,
λ x10 x11 . 4a7ef.. = bc82c.. 4a7ef.. x11 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_ccff4249496414413c3c95467fb8c02c96509ca2826dc03833e7de26e75fcd74 with
4a7ef..,
λ x11 x12 . x10 x12 x11.
The subproof is completed by applying unknownprop_a66a65189a5389c2141d18df52f52fcf5f074fba68040a0bda3b8b81c830611a.
The subproof is completed by applying H3.
set y8 to be λ x8 . y7
Apply L3 with
λ x9 . y8 x9 y7 ⟶ y8 y7 x9 leaving 2 subgoals.
Assume H4: y8 y7 y7.
The subproof is completed by applying H4.
The subproof is completed by applying L3.
Let x4 of type ι → ι → ο be given.
Apply L2 with
λ x5 . x4 x5 y3 ⟶ x4 y3 x5.
Assume H3: x4 y3 y3.
The subproof is completed by applying H3.