| pf |
|---|
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι be given.
Let x5 of type ι → ι be given.
Let x6 of type ι → ι → ο be given.
Let x7 of type ι → ι → ο be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Claim L2: x0 = x1
Apply L1 with λ x10 x11 . x0 = x11.
The subproof is completed by applying unknownprop_65b816444de57457f1c789231a42b642eb46addfdf0a5e485c477bf4a51e7c89 with x0, x2, x4, x6, x8.
Apply and5I with x0 = x1, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11, x8 = x9 leaving 5 subgoals.
The subproof is completed by applying L2.
Let x10 of type ι be given.
Let x11 of type ι be given.
Apply unknownprop_9a5741423aa2dc66d36e7ecf7a37b3fd742da71a02f2cb5aee028428187a5ea4 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x3 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with λ x12 x13 . prim1 x10 x12.
The subproof is completed by applying H3.
Apply L2 with λ x12 x13 . prim1 x11 x12.
The subproof is completed by applying H4.
Apply H0 with λ x12 x13 . e3162.. (f482f.. x13 (4ae4a.. 4a7ef..)) x10 x11 = x3 x10 x11.
Let x12 of type ι → ι → ο be given.
Apply unknownprop_9a5741423aa2dc66d36e7ecf7a37b3fd742da71a02f2cb5aee028428187a5ea4 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 . x12 x14 x13 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x10 of type ι be given.
Apply unknownprop_7e0a7ff7f5f6233fafadf817a30f50626bcc2bcc44229e6ba877803a542777ff with x0, x2, x4, x6, x8, x10, λ x11 x12 . x12 = x5 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with λ x11 x12 . prim1 x10 x11.
The subproof is completed by applying H3.
Apply H0 with λ x11 x12 . f482f.. (f482f.. x12 (4ae4a.. (4ae4a.. 4a7ef..))) x10 = x5 x10.
Let x11 of type ι → ι → ο be given.
Apply unknownprop_7e0a7ff7f5f6233fafadf817a30f50626bcc2bcc44229e6ba877803a542777ff with x1, x3, x5, x7, x9, x10, λ x12 x13 . x11 x13 x12.
The subproof is completed by applying L4.
Let x10 of type ι be given.
Let x11 of type ι be given.
Apply unknownprop_5c8b29a53bcfb2f08adfa0f430a22906136cdc99ef3521728b31c3220ccffea0 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x7 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with λ x12 x13 . prim1 x10 x12.
The subproof is completed by applying H3.
Apply L2 with λ x12 x13 . prim1 x11 x12.
The subproof is completed by applying H4.
Apply H0 with λ x12 x13 . 2b2e3.. (f482f.. x13 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 x11 = x7 x10 x11.
Let x12 of type ο → ο → ο be given.
Apply unknownprop_5c8b29a53bcfb2f08adfa0f430a22906136cdc99ef3521728b31c3220ccffea0 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 : ο . x12 x14 x13 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Apply unknownprop_17176d8a02df5fdd45f1c61e7edd0a0660313bddfe874e4832062f44f1a0675d with x0, x2, x4, x6, x8, λ x10 x11 . x11 = x9.
Apply H0 with λ x10 x11 . f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x9.
Let x10 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_17176d8a02df5fdd45f1c61e7edd0a0660313bddfe874e4832062f44f1a0675d with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
■ |
|