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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 be given.
Let x3 of type ι be given.
Assume H0: Subq x0 x2.
Assume H1: Subq x1 x3.
Let x4 of type ι be given.
Assume H2: prim1 x4 (aae7a.. x0 x1).
Apply unknownprop_c7550417d862f27710857dc7f3a47fd61afe15d66581922367eb5c5641bfab12 with x0, x1, x4, prim1 x4 (aae7a.. x2 x3) leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: ∃ x5 . and (prim1 x5 x0) (x4 = f6917.. x5).
Apply exandE_i with λ x5 . prim1 x5 x0, λ x5 . x4 = f6917.. x5, prim1 x4 (aae7a.. x2 x3) leaving 2 subgoals.
The subproof is completed by applying H3.
Let x5 of type ι be given.
Assume H4: prim1 x5 x0.
Assume H5: x4 = f6917.. x5.
Apply H5 with λ x6 x7 . prim1 x7 (aae7a.. x2 x3).
Apply unknownprop_8f6cc176a3f8bf2c7f1eddd738c1f22ef319b214b1baddc301c61e34c7bade15 with x2, x3, x5.
Apply H0 with x5.
The subproof is completed by applying H4.
Assume H3: ∃ x5 . and (prim1 x5 x1) (x4 = 09364.. x5).
Apply exandE_i with λ x5 . prim1 x5 x1, λ x5 . x4 = 09364.. x5, prim1 x4 (aae7a.. x2 x3) leaving 2 subgoals.
The subproof is completed by applying H3.
Let x5 of type ι be given.
Assume H4: prim1 x5 x1.
Assume H5: x4 = 09364.. x5.
Apply H5 with λ x6 x7 . prim1 x7 (aae7a.. x2 x3).
Apply unknownprop_21bfd05a2dded69408d4a77ad07f3965317c49d7fa73834904d6def11389f597 with x2, x3, x5.
Apply H1 with x5.
The subproof is completed by applying H4.
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