let S be non empty set ; :: thesis: for R being total Relation of S,S
for BASSIGN being non empty Subset of (ModelSP S)
for f being Assign of (CTLModel R,BASSIGN)
for G1, G2 being Subset of S st G1 c= G2 holds
SigFaxTau f,G1,R,BASSIGN c= SigFaxTau f,G2,R,BASSIGN
let R be total Relation of S,S; :: thesis: for BASSIGN being non empty Subset of (ModelSP S)
for f being Assign of (CTLModel R,BASSIGN)
for G1, G2 being Subset of S st G1 c= G2 holds
SigFaxTau f,G1,R,BASSIGN c= SigFaxTau f,G2,R,BASSIGN
let BASSIGN be non empty Subset of (ModelSP S); :: thesis: for f being Assign of (CTLModel R,BASSIGN)
for G1, G2 being Subset of S st G1 c= G2 holds
SigFaxTau f,G1,R,BASSIGN c= SigFaxTau f,G2,R,BASSIGN
let f be Assign of (CTLModel R,BASSIGN); :: thesis: for G1, G2 being Subset of S st G1 c= G2 holds
SigFaxTau f,G1,R,BASSIGN c= SigFaxTau f,G2,R,BASSIGN
let G1, G2 be Subset of S; :: thesis: ( G1 c= G2 implies SigFaxTau f,G1,R,BASSIGN c= SigFaxTau f,G2,R,BASSIGN )
assume G1 c= G2 ; :: thesis: SigFaxTau f,G1,R,BASSIGN c= SigFaxTau f,G2,R,BASSIGN
then for s being Element of S st s |= Tau G1,R,BASSIGN holds
s |= Tau G2,R,BASSIGN by Th34;
then for s being Element of S st s |= Fax f,(Tau G1,R,BASSIGN) holds
s |= Fax f,(Tau G2,R,BASSIGN) by Th36;
hence SigFaxTau f,G1,R,BASSIGN c= SigFaxTau f,G2,R,BASSIGN by Th35; :: thesis: verum