:: deftheorem Def66 defines AddAsWitnessTo FOMODEL4:def 66 :
for S being Language
for D being RuleSet of S
for X being functional set
for phi being Element of ExFormulasOf S holds
( ( X \/ {phi} is D -consistent & (LettersOf S) \ (SymbolsOf ((((AllSymbolsOf S) *) \ {{}}) /\ (X \/ {(head phi)}))) <> {} implies (D,phi) AddAsWitnessTo X = X \/ {((((S -firstChar) . phi), the Element of (LettersOf S) \ (SymbolsOf ((((AllSymbolsOf S) *) \ {{}}) /\ (X \/ {(head phi)})))) -SymbolSubstIn (head phi))} ) & ( ( not X \/ {phi} is D -consistent or not (LettersOf S) \ (SymbolsOf ((((AllSymbolsOf S) *) \ {{}}) /\ (X \/ {(head phi)}))) <> {} ) implies (D,phi) AddAsWitnessTo X = X ) );