Apply functional extensionality with
or,
λ x0 x1 : ο . not (and (not x0) (not x1)).
Let x0 of type ο be given.
Apply functional extensionality with
or x0,
(λ x1 x2 : ο . not (and (not x1) (not x2))) x0.
Let x1 of type ο be given.
Apply prop_ext_2 with
or x0 x1,
(λ x2 x3 : ο . not (and (not x2) (not x3))) x0 x1 leaving 2 subgoals.
Apply H1 with
False.
Apply H0 with
False leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply xm with
x0,
or x0 x1 leaving 2 subgoals.
Assume H1: x0.
Apply orIL with
x0,
x1.
The subproof is completed by applying H1.
Apply xm with
x1,
or x0 x1 leaving 2 subgoals.
Assume H2: x1.
Apply orIR with
x0,
x1.
The subproof is completed by applying H2.
Apply H0 with
or x0 x1.
Apply andI with
not x0,
not x1 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.