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 ο be given.
Assume H4: x1 = x2 ⟶ x3.
Apply xm with
x1 = x2,
x3 leaving 2 subgoals.
Assume H6: x1 = x2.
Apply H4.
The subproof is completed by applying H6.
Assume H6: x1 = x2 ⟶ ∀ x4 : ο . x4.
Apply RealsStruct_leq_linear with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply H3.
Apply andI with
RealsStruct_leq x0 x1 x2,
x1 = x2 ⟶ ∀ x4 : ο . x4 leaving 2 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H6.
Apply H5.
Apply andI with
RealsStruct_leq x0 x2 x1,
x2 = x1 ⟶ ∀ x4 : ο . x4 leaving 2 subgoals.
The subproof is completed by applying H7.
Apply neq_i_sym with
x1,
x2.
The subproof is completed by applying H6.