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.
Assume H2:
∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = x3 x4 x5.
Apply explicit_Group_repindep_imp with
x1,
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H0.
Apply prop_ext_2 with
a0fbb.. x1 x2 x0,
a0fbb.. x1 x3 x0 leaving 2 subgoals.
Apply unknownprop_dd9d001170691a926e615e822419029e8cdf15113e6164036a61cfffcea59820 with
x0,
x1,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_dd9d001170691a926e615e822419029e8cdf15113e6164036a61cfffcea59820 with
x0,
x1,
x3,
x2 leaving 3 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying H1.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι → ι → ο be given.
Apply H2 with
x4,
x5,
λ x7 x8 . x6 x8 x7 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.