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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 → ο be given.
Let x7 of type ι → ι → ο be given.
Let x8 of type ι → ο be given.
Let x9 of type ι → ο be given.
Assume H0: 9f84a.. x0 x2 x4 x6 x8 = 9f84a.. 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_d301693eb1fa0da7f271198093e9f6d03844da17df8460c814a3c7e04330e1bd 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_d301693eb1fa0da7f271198093e9f6d03844da17df8460c814a3c7e04330e1bd 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_f9ab74e6a825d231a8f13599dca1474efce0a9e0d29b33944ec2c0009892b1c3 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_f9ab74e6a825d231a8f13599dca1474efce0a9e0d29b33944ec2c0009892b1c3 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_c1ac95df319708a0a9776f296ca0a8170fd3188b34ed6996bb4a1132ca15ce9d 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.
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 . 2b2e3.. (f482f.. x13 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 x11 = x7 x10 x11.
Let x12 of type ο → ο → ο be given.
Apply unknownprop_c1ac95df319708a0a9776f296ca0a8170fd3188b34ed6996bb4a1132ca15ce9d 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.
Let x10 of type ι be given.
Assume H3: prim1 ... ....
...
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