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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 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.
Assume H0: d89a7.. x0 x2 x4 x6 = d89a7.. x1 x3 x5 x7.
Claim L1: x1 = f482f.. (d89a7.. x0 x2 x4 x6) 4a7ef..
Apply unknownprop_15d079a0a6a20101c1b8e62b8bb1753d61ddefbe36c6e4ebfd44b2e3d3797833 with d89a7.. x0 x2 x4 x6, x1, x3, x5, x7.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with λ x8 x9 . x0 = x9.
The subproof is completed by applying unknownprop_ba194c2202ced89f547acbeed926c5ea6a29f7cca72cc88e80d18b7ebbb1e52d 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 ⟶ x4 x8 = x5 x8, ∀ 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_325bcb5a256ab9329e80a14f794ea1b267596485f1c43f7b00c5997e3eb3ce72 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_325bcb5a256ab9329e80a14f794ea1b267596485f1c43f7b00c5997e3eb3ce72 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.
Apply unknownprop_1e75cd0b3307fe13c67a0c1db282e2e688fb42fc347d98829e01d0ac65464433 with x0, x2, x4, x6, x8, λ x9 x10 . x10 = x5 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4: prim1 x8 x1
Apply L2 with λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with λ x9 x10 . f482f.. (f482f.. x10 (4ae4a.. (4ae4a.. 4a7ef..))) x8 = x5 x8.
Let x9 of type ι → ι → ο be given.
Apply unknownprop_1e75cd0b3307fe13c67a0c1db282e2e688fb42fc347d98829e01d0ac65464433 with x1, x3, x5, x7, x8, λ x10 x11 . x9 x11 x10.
The subproof is completed by applying L4.
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_7150e92e55bd9c994083b0e205f066c8c716fd2d7db929fded102f4c0566f20f with x0, x2, x4, x6, x8, x9, λ x10 x11 : ο . 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 . 2b2e3.. (f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 x9 = x7 x8 x9.
Let x10 of type ο → ο → ο be given.
Apply unknownprop_7150e92e55bd9c994083b0e205f066c8c716fd2d7db929fded102f4c0566f20f with x1, x3, x5, x7, x8, x9, λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
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