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.
Claim L4: ∀ x6 : ι → ο . x6 y5 ⟶ x6 y4
Let x6 of type ι → ο be given.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with
x2,
x3,
bc82c.. y4 y5,
λ x7 . x6 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
y4,
y5 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with
bc82c.. x2 x3,
y4,
y5,
λ x7 . x6 leaving 4 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Claim L5: ∀ x9 : ι → ο . x9 y8 ⟶ x9 y7
Let x9 of type ι → ο be given.
set y10 to be λ x10 . x9
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with
y4,
y5,
x6,
λ x12 x13 . y11 x13 x12 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H5.
set y9 to be λ x9 . y8
Apply L5 with
λ x10 . y9 x10 y8 ⟶ y9 y8 x10 leaving 2 subgoals.
Assume H6: y9 y8 y8.
The subproof is completed by applying H6.
The subproof is completed by applying L5.
Let x6 of type ι → ι → ο be given.
Apply L4 with
λ x7 . x6 x7 y5 ⟶ x6 y5 x7.
Assume H5: x6 y5 y5.
The subproof is completed by applying H5.