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.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_36f11cc7571fa2487251d5a7c42936b64e63f594759a4c4f588173d9cd2aec53 with
bc82c.. x0 x1,
x6,
bc82c.. x2 (bc82c.. x3 x4) leaving 4 subgoals.
The subproof is completed by applying L12.
The subproof is completed by applying H6.
The subproof is completed by applying L13.
Apply unknownprop_fb545b225a42993d98e0d062b6c9208b8321e87814f4e26de3418c134068c2c8 with
bc82c.. (bc82c.. x0 x1) x6,
bc82c.. x0 (bc82c.. x2 (bc82c.. x3 x5)),
bc82c.. (bc82c.. x2 (bc82c.. x3 x4)) x6 leaving 5 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
bc82c.. x0 x1,
x6 leaving 2 subgoals.
The subproof is completed by applying L12.
The subproof is completed by applying H6.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
x0,
bc82c.. x2 (bc82c.. x3 x5) leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L14.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
bc82c.. x2 (bc82c.. x3 x4),
x6 leaving 2 subgoals.
The subproof is completed by applying L13.
The subproof is completed by applying H6.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with
x0,
x1,
x6,
λ x8 x9 . 099f3.. x8 (bc82c.. x0 (bc82c.. x2 (bc82c.. x3 x5))) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H6.
Apply unknownprop_443bf25288cf39bc78395680f7fe50ad1a2a509c594b439821412f6af4f99866 with
x1,
x6,
λ x8 x9 . 099f3.. (bc82c.. x0 x9) (bc82c.. x0 (bc82c.. x2 (bc82c.. x3 x5))) leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H6.
Apply unknownprop_50ea7279d1527aec8642473c7707da12238935f258091dd2df6f6eae075c74e1 with
x0,
bc82c.. x6 x1,
bc82c.. x2 (bc82c.. x3 x5) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L15.
The subproof is completed by applying L14.
The subproof is completed by applying L11.
set y8 to be ...
set y9 to be ...
Claim L17: ∀ x10 : ι → ο . x10 y9 ⟶ x10 y8
Let x10 of type ι → ο be given.
set y11 to be ...
set y12 to be ...
set y13 to be ...
Apply L18 with
λ x14 . y13 x14 y12 ⟶ y13 y12 x14 leaving 2 subgoals.
Assume H19: y13 y12 y12.
The subproof is completed by applying H19.
set y14 to be ...
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with
bc82c.. x7 y8,
y9,
y11,
λ x15 x16 . y14 x16 x15 leaving 4 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
x7,
y8 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H7.
set y15 to be ...
set y16 to be ...
Claim L19: ∀ x17 : ι → ο . x17 y16 ⟶ x17 y15
Let x17 of type ι → ο be given.
set y17 to be λ x17 . y16
Apply L19 with
λ x18 . y17 x18 y16 ⟶ y17 y16 x18 leaving 2 subgoals.
Assume H20: y17 y16 y16.
The subproof is completed by applying H20.
The subproof is completed by applying L19.
Let x10 of type ι → ι → ο be given.
Apply L17 with
λ x11 . x10 x11 y9 ⟶ x10 y9 x11.
Assume H18: x10 y9 y9.
The subproof is completed by applying H18.
Apply L16 with
λ x8 x9 . 099f3.. x9 (bc82c.. (bc82c.. x2 (bc82c.. x3 x4)) x6).
Apply L17 with
λ x8 x9 . 099f3.. (bc82c.. (bc82c.. x2 x3) (bc82c.. x0 x5)) x9.
Apply unknownprop_50ea7279d1527aec8642473c7707da12238935f258091dd2df6f6eae075c74e1 with
bc82c.. x2 x3,
bc82c.. x0 x5,
bc82c.. x6 x4 leaving 4 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
x0,
x5 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H5.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
x6,
x4 leaving 2 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H4.
The subproof is completed by applying H8.