let Al be QC-alphabet ; :: thesis: for f being FinSequence of CQC-WFF Al holds Ant (f ^ <*(VERUM Al)*>) |= Suc (f ^ <*(VERUM Al)*>)
let f be FinSequence of CQC-WFF Al; :: thesis: Ant (f ^ <*(VERUM Al)*>) |= Suc (f ^ <*(VERUM Al)*>)
let A be non empty set ; :: according to CALCUL_1:def 15 :: thesis: for J being interpretation of Al,A
for v being Element of Valuations_in (Al,A) st J,v |= Ant (f ^ <*(VERUM Al)*>) holds
J,v |= Suc (f ^ <*(VERUM Al)*>)
let J be interpretation of Al,A; :: thesis: for v being Element of Valuations_in (Al,A) st J,v |= Ant (f ^ <*(VERUM Al)*>) holds
J,v |= Suc (f ^ <*(VERUM Al)*>)
let v be Element of Valuations_in (Al,A); :: thesis: ( J,v |= Ant (f ^ <*(VERUM Al)*>) implies J,v |= Suc (f ^ <*(VERUM Al)*>) )
assume J,v |= Ant (f ^ <*(VERUM Al)*>) ; :: thesis: J,v |= Suc (f ^ <*(VERUM Al)*>)
Suc (f ^ <*(VERUM Al)*>) = VERUM Al by Th5;
hence J,v |= Suc (f ^ <*(VERUM Al)*>) by VALUAT_1:32; :: thesis: verum