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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.
Apply unpack_b_o_eq with λ x4 . λ x5 : ι → ι → ι . unpack_b_o (pack_b x0 x2) (λ x6 . λ x7 : ι → ι → ι . and (and (pack_b x0 x2 = pack_b x6 x5) (Group (pack_b x6 x5))) (x6 ⊆ x4)), x1, x3, λ x4 x5 : ο . x5 = and (and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3))) (x0 ⊆ x1) leaving 2 subgoals.
Let x4 of type ι → ι → ι be given.
Assume H0: ∀ x5 . x5 ∈ x1 ⟶ ∀ x6 . x6 ∈ x1 ⟶ x3 x5 x6 = x4 x5 x6.
Apply unknownprop_849033760b3699131a909f0571933f68e8c142b844e9ed0e264c912c9933afc7 with x0, x1, x2, x3, λ x5 x6 : ο . unpack_b_o (pack_b x0 x2) (λ x7 . λ x8 : ι → ι → ι . and (and (pack_b x0 x2 = pack_b x7 x4) (Group (pack_b x7 x4))) (x7 ⊆ x1)) = x6.
Apply unknownprop_849033760b3699131a909f0571933f68e8c142b844e9ed0e264c912c9933afc7 with x0, x1, x2, x4, λ x5 x6 : ο . x6 = and (and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3))) (x0 ⊆ x1).
Claim L1: ...
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Apply prop_ext_2 with and (and (pack_b x0 x2 = pack_b x0 x4) (Group (pack_b x0 x4))) (x0 ⊆ x1), and (and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3))) (x0 ⊆ x1) leaving 2 subgoals.
Assume H2: and (and (pack_b x0 x2 = pack_b x0 x4) (Group (pack_b x0 x4))) (x0 ⊆ x1).
Apply H2 with and (and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3))) (x0 ⊆ x1).
Assume H3: and (pack_b x0 x2 = pack_b x0 x4) (Group (pack_b x0 x4)).
Assume H4: x0 ⊆ x1.
Apply L1 with λ x5 x6 . and (and (pack_b x0 x2 = x6) (Group x6)) (x0 ⊆ x1) leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
Assume H2: and (and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3))) (x0 ⊆ x1).
Apply H2 with and (and (pack_b x0 x2 = pack_b x0 x4) (Group (pack_b x0 x4))) (x0 ⊆ x1).
Assume H3: and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3)).
Assume H4: x0 ⊆ x1.
Apply L1 with λ x5 x6 . and (and (pack_b x0 x2 = x5) (Group x5)) (x0 ⊆ x1) leaving 2 subgoals.
The subproof is completed by applying H4.
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