theorem Th54: :: MODELC_3:54

for H, v being LTL-formula
for q being sequence of (LTLStates v) st H is Until & H in the LTLold of (CastNode ((q . 1),v)) & ( for i being Nat holds CastNode ((q . (i + 1)),v) is_next_of CastNode ((q . i),v) ) & ex i being Nat st
( i >= 1 & not ( H in the LTLold of (CastNode ((q . i),v)) & the_left_argument_of H in the LTLold of (CastNode ((q . i),v)) & not the_right_argument_of H in the LTLold of (CastNode ((q . i),v)) ) ) holds
ex j being Nat st
( j >= 1 & the_right_argument_of H in the LTLold of (CastNode ((q . j),v)) & ( for i being Nat st 1 <= i & i < j holds
( H in the LTLold of (CastNode ((q . i),v)) & the_left_argument_of H in the LTLold of (CastNode ((q . i),v)) ) ) )