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 ι be given.
Apply dneg with
or (atleastp (ordsucc x0) x2) (atleastp (ordsucc x1) x3).
Apply unknownprop_45d11dce2d0b092bd17c01d64c29c5885c90b43dc7cb762c6d6ada999ea508c5 with
x0,
x2,
False leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_45d11dce2d0b092bd17c01d64c29c5885c90b43dc7cb762c6d6ada999ea508c5 with
x1,
x3,
False leaving 3 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_8a6bdce060c93f04626730b6e01b099cc0487102a697e253c81b39b9a082262d with
add_nat x0 x1 leaving 2 subgoals.
Apply add_nat_p with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply atleastp_tra with
ordsucc (add_nat x0 x1),
binunion x2 x3,
add_nat x0 x1 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply atleastp_tra with
binunion x2 x3,
setsum x0 x1,
add_nat x0 x1 leaving 2 subgoals.
Apply unknownprop_8805a75f81012de0423e9173532fc074fb73b80e451597fde52287a4721fb204 with
x2,
x3,
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Apply equip_atleastp with
setsum x0 x1,
add_nat x0 x1.
Apply equip_sym with
add_nat x0 x1,
setsum x0 x1.
Apply unknownprop_80fb4e499c5b9d344e7e79a37790e81cc16e6fd6cd87e88e961f3c8c4d6d418f with
x0,
x1,
x0,
x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying equip_ref with x0.
The subproof is completed by applying equip_ref with x1.