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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: ordinal x0.
Let x1 of type ι → ο be given.
Assume H1: ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x2 ⟶ x1 x2 ⟶ x1 x3.
Apply andI with TransSet (1216a.. x0 (λ x2 . x1 x2)), ∀ x2 . prim1 x2 (1216a.. x0 (λ x3 . x1 x3)) ⟶ TransSet x2 leaving 2 subgoals.
Let x2 of type ι be given.
Assume H2: prim1 x2 (1216a.. x0 (λ x3 . x1 x3)).
Let x3 of type ι be given.
Assume H3: prim1 x3 x2.
Apply unknownprop_e4362c04e65a765de9cf61045b78be0adc0f9e51a17754420e1088df0891ff67 with x0, x1, x2, prim1 x3 (1216a.. x0 (λ x4 . x1 x4)) leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H4: prim1 x2 x0.
Assume H5: x1 x2.
Apply unknownprop_1dada0fb38ff7f9b45b564ad11d6295d93250427446875218f17ee62431454a6 with x0, x1, x3 leaving 2 subgoals.
Apply H0 with prim1 x3 x0.
Assume H6: TransSet x0.
Assume H7: ∀ x4 . prim1 x4 x0 ⟶ TransSet x4.
Apply H6 with x2, x3 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
Apply H1 with x2, x3 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
Let x2 of type ι be given.
Assume H2: prim1 x2 (1216a.. x0 (λ x3 . x1 x3)).
Claim L3: prim1 x2 x0
Apply unknownprop_78dd4d18930f8cdb1d353eca6deb6db797599b58a01b747c9a28b7030299025c with x0, x1, x2.
The subproof is completed by applying H2.
Apply ordinal_Hered with x0, x2, TransSet x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L3.
Assume H4: TransSet x2.
Assume H5: ∀ x3 . prim1 x3 x2 ⟶ TransSet x3.
The subproof is completed by applying H4.
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