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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Let x2 of type ο be given.
Assume H2: ∀ x3 x4 . 02b90.. x3 x4 ⟶ (∀ x5 . prim1 x5 x3 ⟶ ∀ x6 : ο . (∀ x7 . prim1 x7 (23e07.. x0) ⟶ ∀ x8 . prim1 x8 (23e07.. x1) ⟶ x5 = bc82c.. (e6316.. x7 x1) (bc82c.. (e6316.. x0 x8) (f4dc0.. (e6316.. x7 x8))) ⟶ x6) ⟶ (∀ x7 . prim1 x7 (5246e.. x0) ⟶ ∀ x8 . prim1 x8 (5246e.. x1) ⟶ x5 = bc82c.. (e6316.. x7 x1) (bc82c.. (e6316.. x0 x8) (f4dc0.. (e6316.. x7 x8))) ⟶ x6) ⟶ x6) ⟶ (∀ x5 . prim1 x5 (23e07.. x0) ⟶ ∀ x6 . prim1 x6 (23e07.. x1) ⟶ prim1 (bc82c.. (e6316.. x5 x1) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))) x3) ⟶ (∀ x5 . prim1 x5 (5246e.. x0) ⟶ ∀ x6 . prim1 x6 (5246e.. x1) ⟶ prim1 (bc82c.. (e6316.. x5 x1) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))) x3) ⟶ (∀ x5 . prim1 x5 x4 ⟶ ∀ x6 : ο . (∀ x7 . prim1 x7 (23e07.. x0) ⟶ ∀ x8 . prim1 x8 (5246e.. x1) ⟶ x5 = bc82c.. (e6316.. x7 x1) (bc82c.. (e6316.. x0 x8) (f4dc0.. (e6316.. x7 x8))) ⟶ x6) ⟶ (∀ x7 . prim1 x7 (5246e.. x0) ⟶ ∀ x8 . prim1 x8 (23e07.. x1) ⟶ x5 = bc82c.. (e6316.. x7 x1) (bc82c.. (e6316.. x0 x8) (f4dc0.. (e6316.. x7 x8))) ⟶ x6) ⟶ x6) ⟶ (∀ x5 . prim1 x5 (23e07.. x0) ⟶ ∀ x6 . prim1 x6 (5246e.. x1) ⟶ prim1 (bc82c.. (e6316.. x5 x1) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))) x4) ⟶ (∀ x5 . prim1 x5 (5246e.. x0) ⟶ ∀ x6 . prim1 x6 (23e07.. x1) ⟶ prim1 (bc82c.. (e6316.. x5 x1) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))) x4) ⟶ e6316.. x0 x1 = 02a50.. x3 x4 ⟶ x2.
Apply unknownprop_f4c47e876b581d8d577d2c853ba9f380382521b2987b498decb65a17a2733264 with x0, x1, x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H3: ∀ x5 . ... ⟶ ∀ x6 : ο . ... ⟶ (∀ x7 . ... ⟶ ∀ x8 . prim1 x8 (5246e.. x1) ⟶ x5 = bc82c.. (e6316.. x7 x1) (bc82c.. (e6316.. x0 x8) (f4dc0.. (e6316.. x7 x8))) ⟶ x6) ⟶ x6.
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