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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.
Assume H0: 7c612.. x0 x2 x4 x6 = 7c612.. x1 x3 x5 x7.
Claim L1: x1 = f482f.. (7c612.. x0 x2 x4 ...) ...
...
Claim L2: x0 = x1
Apply L1 with λ x8 x9 . x0 = x9.
The subproof is completed by applying unknownprop_8f65da788a93ff89d95bcf516abc29daa711f2c16faefefcaad5ba81f2e71786 with x0, x2, x4, x6.
Apply and4I with x0 = x1, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x6 x8 x9 = x7 x8 x9 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Assume H3: prim1 x8 x0.
Let x9 of type ι be given.
Assume H4: prim1 x9 x0.
Apply unknownprop_ff4535e6de7d81b5e64319b54276975d755c6038dfc6568b8eaad6de9e67f064 with x0, x2, x4, x6, x8, x9, λ x10 x11 . x11 = x3 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x8 x1
Apply L2 with λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Claim L6: prim1 x9 x1
Apply L2 with λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with λ x10 x11 . e3162.. (f482f.. x11 (4ae4a.. 4a7ef..)) x8 x9 = x3 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_ff4535e6de7d81b5e64319b54276975d755c6038dfc6568b8eaad6de9e67f064 with x1, x3, x5, x7, x8, x9, λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Assume H3: prim1 x8 x0.
Let x9 of type ι be given.
Assume H4: prim1 x9 x0.
Apply unknownprop_d91c9a6f9c15a2c6b9d2b80e56f063e4e1af105da6d9f1d5f7ab2c269bb9687a with x0, x2, x4, x6, x8, x9, λ x10 x11 . x11 = x5 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x8 x1
Apply L2 with λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Claim L6: prim1 x9 x1
Apply L2 with λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with λ x10 x11 . e3162.. (f482f.. x11 (4ae4a.. (4ae4a.. 4a7ef..))) x8 x9 = x5 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_d91c9a6f9c15a2c6b9d2b80e56f063e4e1af105da6d9f1d5f7ab2c269bb9687a with x1, x3, x5, x7, x8, x9, λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Assume H3: prim1 x8 x0.
Let x9 of type ι be given.
Assume H4: prim1 x9 x0.
Apply unknownprop_d90cbda69461be2219583389e1055578190fbc4e0c943c03394d871429ab3a0a with x0, x2, x4, x6, x8, x9, λ x10 x11 . x11 = x7 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x8 x1
Apply L2 with λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Claim L6: prim1 x9 x1
Apply L2 with λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with λ x10 x11 . e3162.. (f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 x9 = x7 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_d90cbda69461be2219583389e1055578190fbc4e0c943c03394d871429ab3a0a with x1, x3, x5, x7, x8, x9, λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
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