Let x0 of type ι be given.

Assume H0: 8f2ce.. x0.

Apply H0 with λ x1 . x1 = 0d9e7.. (f482f.. x1 4a7ef..) (2b2e3.. (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).

Let x1 of type ι be given.

Let x2 of type ι → ι → ο be given.

Let x3 of type ι → ι → ο be given.

Let x4 of type ι be given.

Assume H1: prim1 x4 x1.

Let x5 of type ι be given.

Assume H2: prim1 x5 x1.

Apply unknownprop_e30283de5e06c43feeedf7ea28f31302b2b9c54b266fa07d32b4a8647937baf2 with x1, x2, x3, x4, x5, λ x6 x7 . 0d9e7.. x1 x2 x3 x4 x5 = 0d9e7.. x6 (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).

Apply unknownprop_a74292f97535bb6becd1b270890a3d3a46394d140b4094c8913e6d9ae8b70b41 with x1, x2, x3, x4, x5, λ x6 x7 . 0d9e7.. x1 x2 x3 x4 x5 = 0d9e7.. x1 (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).

Apply unknownprop_5375e18e6b66f3447ee2d8a0cd062eefda6605eebcb4137b7f34fa84355c3421 with x1, x2, x3, x4, x5, λ x6 x7 . 0d9e7.. x1 x2 x3 x4 x5 = 0d9e7.. x1 (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) x4 x6.

Apply unknownprop_74c451085c21740d3da63ab1822c966d60b565e73d4b83eb972f1511a40a0f4d with x1, x2, 2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), x3, 2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), x4, x5 leaving 2 subgoals.

Let x6 of type ι be given.

Assume H3: prim1 x6 x1.

Let x7 of type ι be given.

Assume H4: prim1 x7 x1.

Apply unknownprop_bf3a81e508dd5bb7ebd0d922aa476a754ab01577312522215ed550d7a6c72b06 with x1, x2, x3, x4, x5, x6, x7, λ x8 x9 : ο . iff (x2 x6 x7) x8 leaving 3 subgoals.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

The subproof is completed by applying iff_refl with x2 x6 x7.

Let x6 of type ι be given.

Assume H3: prim1 x6 x1.

Let x7 of type ι be given.

Assume H4: prim1 x7 x1.

Apply unknownprop_d478b39a50d95c7bfa6335b02cb600d8bcf61e1565ccfaa353e4998231071c0e with x1, x2, x3, x4, x5, x6, x7, λ x8 x9 : ο . iff (x3 x6 x7) x8 leaving 3 subgoals.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

The subproof is completed by applying iff_refl with x3 x6 x7.

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Proofgold Proof