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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: 303f6.. x0.
Apply H0 with λ x1 . x1 = 3da2d.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Assume H1: ∀ x3 . prim1 x3 x1 ⟶ ∀ x4 . prim1 x4 x1 ⟶ prim1 (x2 x3 x4) x1.
Let x3 of type ι → ι be given.
Assume H2: ∀ x4 . prim1 x4 x1 ⟶ prim1 (x3 x4) x1.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Apply unknownprop_59cba52dae762e3a37e13385259603b56c45f99300f789bf1965c606d0d51c31 with x1, x2, x3, x4, x5, λ x6 x7 . 3da2d.. x1 x2 x3 x4 x5 = 3da2d.. x6 (e3162.. (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))).
Apply unknownprop_af12a6518e070999041dea1b7a26135219cd0655d58bf3ed6c644a9bd53f03cc with x1, x2, e3162.. (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), x3, f482f.. (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), x4, decode_p (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))), x5, decode_p (f482f.. (3da2d.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) leaving 4 subgoals.
The subproof is completed by applying unknownprop_b300dc0e6196169572027279aabac17f8c152b677d9ff2fd9266205f99010d7d with x1, x2, x3, x4, x5.
The subproof is completed by applying unknownprop_18b4978245363139c79319afc6a1fd980fb5e61013e19858dcbc5f8552aa6580 with x1, x2, x3, x4, x5.
Let x6 of type ι be given.
Assume H3: prim1 x6 x1.
Apply unknownprop_cbd33d489eeb7d204f5b4295480477cdd2c260d24ff5e2145d06f3d38da2cd2a with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x4 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x4 x6.
Let x6 of type ι be given.
Assume H3: prim1 x6 x1.
Apply unknownprop_1805de6db1481c8fd0f6bd31bdce3dd3c0148e9c4bc0e70f8d801710dbd35e36 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x5 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x5 x6.
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