theorem WALDistri: :: LATWAL_1:18

for L being non empty LattStr st ( for v0 being Element of L holds v0 "/\" v0 = v0 ) & ( for v1, v0 being Element of L holds v0 "/\" v1 = v1 "/\" v0 ) & ( for v0 being Element of L holds v0 "\/" v0 = v0 ) & ( for v1, v0 being Element of L holds v0 "\/" v1 = v1 "\/" v0 ) & ( for v2, v1, v0 being Element of L holds ((v0 "\/" v1) "/\" (v2 "\/" v1)) "/\" v1 = v1 ) & ( for v2, v1, v0 being Element of L holds ((v0 "/\" v1) "\/" (v2 "/\" v1)) "\/" v1 = v1 ) & ( for v1, v0 being Element of L holds v0 "/\" (v0 "\/" v1) = v0 ) & ( for v0, v2, v1 being Element of L holds v0 "\/" (v1 "/\" v2) = (v0 "\/" v1) "/\" (v0 "\/" v2) ) holds
for v0, v1, v2 being Element of L holds (v0 "\/" v1) "\/" v2 = v0 "\/" (v1 "\/" v2)