 reserve L for non empty LattStr;
 reserve v64,v65,v66,v67,v103,v3,v102,v101,v100,v2,v1,v0 for Element of L;

theorem Seventh:
L is join-absorbing &
(for v0,v2,v1 holds (v0"/\"(v1"\/"v2))=((v2"/\"v0)"\/"(v1"/\"v0)))
implies for v0,v1,v2 holds v0"/\"(v1"\/"v2)=(v0"/\"v1)"\/"(v0"/\"v2)
proof
assume A3: L is join-absorbing;

assume A4: for v0,v2,v1 holds (v0"/\"(v1"\/"v2))=((v2"/\"v0)"\/"(v1"/\"v0));

A72: for v0,v2,v1 holds (v0"/\"(v1"\/"v2))=((v1"/\"v0)"\/"(v2"/\"v0))
proof let v0,v2,v1;
((v2"/\"v0)"\/"(v1"/\"v0))=(v0"/\"(v1"\/"v2)) by A4;
hence thesis by A3,A4,JoinCom;
end;

A79: for v66,v64,v65 holds ((v65"/\"v64)"\/"(v66"/\"v65))=(v65"/\"(v64"\/"v66))
proof let v66,v64,v65;
(v64"/\"v65)=(v65"/\"v64) by A3,A4,MeetCom;
hence thesis by A72;
end;

let v0,v1,v2;
v0"/\"(v1"\/"v2)=(v0"/\"v1)"\/"(v2"/\"v0) by A79
.=(v0"/\"v1)"\/"(v0"/\"v2) by A3,A4,MeetCom;
hence thesis;
end;
