let f be FinSequence of CQC-WFF ; :: thesis: ( Suc f is_tail_of Ant f implies Ant f |= Suc f )
assume Suc f is_tail_of Ant f ; :: thesis: Ant f |= Suc f
then ex i being Element of NAT st
( i in dom (Ant f) & (Ant f) . i = Suc f ) by Lm1;
then A1: Suc f in rng (Ant f) by FUNCT_1:3;
let A be non empty set ; :: according to CALCUL_1:def 15 :: thesis: for J being interpretation of A
for v being Element of Valuations_in A st J,v |= Ant f holds
J,v |= Suc f
let J be interpretation of A; :: thesis: for v being Element of Valuations_in A st J,v |= Ant f holds
J,v |= Suc f
let v be Element of Valuations_in A; :: thesis: ( J,v |= Ant f implies J,v |= Suc f )
assume J,v |= rng (Ant f) ; :: according to CALCUL_1:def 14 :: thesis: J,v |= Suc f
hence J,v |= Suc f by A1, Def11; :: thesis: verum