theorem TBA2: :: LATTBA_1:15

for B being Boolean Lattice st ( for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = ((v0 "\/" v1) "/\" (v1 "\/" v2)) "/\" (v0 "\/" v2) ) & ( for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v2) = (v0 "\/" v1) "/\" (v0 "\/" v2) ) & ( for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" v2) = (v0 "/\" v1) "\/" (v0 "/\" v2) ) & ( for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "\/" v2 = v0 "\/" (v1 "\/" v2) ) & ( for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" v2 = v0 "/\" (v1 "/\" v2) ) holds
for v1, v2, v3, v4 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v2,v4) = Tern (v1,v2,(Tern (v3,v2,v4)))