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Proofgold Proof

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 → ι be given.
Let x5 of type ι → ι → ι be given.
Let x6 of type ι → ι → ι be given.
Let x7 of type ι → ι → ι be given.
Let x8 of type ι → ι be given.
Let x9 of type ι → ι be given.
Assume H0: 39199.. x0 x2 x4 x6 x8 = 39199.. x1 x3 x5 x7 x9.
Claim L1: ...
...
Claim L2: ...
...
Apply and5I with x0 = x1, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10 leaving 5 subgoals.
The subproof is completed by applying L2.
Let x10 of type ι be given.
Assume H3: prim1 x10 x0.
Let x11 of type ι be given.
Assume H4: prim1 x11 x0.
Apply unknownprop_93ad6d9e989b43148688f9a96022108d8fdf2fbb96408fca4e828dbfbae29330 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.
Claim L5: prim1 x10 x1
Apply L2 with λ x12 x13 . prim1 x10 x12.
The subproof is completed by applying H3.
Claim L6: prim1 x11 x1
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_93ad6d9e989b43148688f9a96022108d8fdf2fbb96408fca4e828dbfbae29330 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.
Assume H3: prim1 x10 x0.
Let x11 of type ι be given.
Assume H4: prim1 x11 x0.
Apply unknownprop_6dd8f55228cd05752343b8ca499fb011022efaaaa36500a4a4d7ce24e9f31c71 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x5 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x10 x1
Apply L2 with λ x12 x13 . prim1 x10 x12.
The subproof is completed by applying H3.
Claim L6: prim1 x11 x1
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.. (4ae4a.. 4a7ef..))) x10 x11 = x5 x10 x11.
Let x12 of type ι → ι → ο be given.
Apply unknownprop_6dd8f55228cd05752343b8ca499fb011022efaaaa36500a4a4d7ce24e9f31c71 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.
Assume H3: prim1 x10 x0.
Let x11 of type ι be given.
Assume H4: prim1 x11 x0.
Apply unknownprop_4af70ca0b99321d573ec535c595ae3567a5a5d4e2f63e06366bc0778b1598496 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x7 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x10 x1
Apply L2 with λ x12 x13 . prim1 x10 x12.
The subproof is completed by applying H3.
Claim L6: prim1 x11 x1
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.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 x11 = x7 x10 x11.
Let x12 of type ι → ι → ο be given.
Apply unknownprop_4af70ca0b99321d573ec535c595ae3567a5a5d4e2f63e06366bc0778b1598496 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.
Assume H3: prim1 ... ....
...
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