Apply functional extensionality with
λ x0 x1 : ο . x0 ⟶ x1,
λ x0 x1 : ο . or (not x0) x1.
Let x0 of type ο be given.
Apply functional extensionality with
(λ x1 x2 : ο . x1 ⟶ x2) x0,
(λ x1 x2 : ο . or (not x1) x2) x0.
Let x1 of type ο be given.
Apply prop_ext_2 with
(λ x2 x3 : ο . x2 ⟶ x3) x0 x1,
(λ x2 x3 : ο . or (not x2) x3) x0 x1 leaving 2 subgoals.
Assume H0: x0 ⟶ x1.
Apply xm with
x0,
or (not x0) x1 leaving 2 subgoals.
Assume H1: x0.
Apply orIR with
not x0,
x1.
Apply H0.
The subproof is completed by applying H1.
Apply orIL with
not x0,
x1.
The subproof is completed by applying H1.
Assume H0:
or (not x0) x1.
Apply H0 with
(λ x2 x3 : ο . x2 ⟶ x3) x0 x1 leaving 2 subgoals.
Assume H2: x0.
Apply H1 with
x1.
The subproof is completed by applying H2.
Assume H1: x1.
Assume H2: x0.
The subproof is completed by applying H1.