Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unpack_b_b_r_e_e_o_eq with
λ x6 . λ x7 x8 : ι → ι → ι . λ x9 : ι → ι → ο . λ x10 x11 . explicit_OrderedField x6 x10 x11 x7 x8 x9,
x0,
x1,
x2,
x3,
x4,
x5.
Let x6 of type ι → ι → ι be given.
Assume H0: ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x1 x7 x8 = x6 x7 x8.
Let x7 of type ι → ι → ι be given.
Assume H1: ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x2 x8 x9 = x7 x8 x9.
Let x8 of type ι → ι → ο be given.
Assume H2:
∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ iff (x3 x9 x10) (x8 x9 x10).
Let x9 of type ο → ο → ο be given.
Apply prop_ext with
explicit_OrderedField x0 x4 x5 x1 x2 x3,
explicit_OrderedField x0 x4 x5 x6 x7 x8,
λ x10 x11 : ο . x9 x11 x10.
Apply explicit_OrderedField_repindep with
x0,
x4,
x5,
x1,
x2,
x3,
x6,
x7,
x8 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.