let H be CTL-formula; :: thesis: for S being non empty set
for R being total Relation of S,S
for s being Element of S
for BASSIGN being non empty Subset of (ModelSP S)
for kai being Function of atomic_WFF, the BasicAssign of (BASSModel (R,BASSIGN)) holds
( s,kai |= EX H iff ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) )
let S be non empty set ; :: thesis: for R being total Relation of S,S
for s being Element of S
for BASSIGN being non empty Subset of (ModelSP S)
for kai being Function of atomic_WFF, the BasicAssign of (BASSModel (R,BASSIGN)) holds
( s,kai |= EX H iff ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) )
let R be total Relation of S,S; :: thesis: for s being Element of S
for BASSIGN being non empty Subset of (ModelSP S)
for kai being Function of atomic_WFF, the BasicAssign of (BASSModel (R,BASSIGN)) holds
( s,kai |= EX H iff ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) )
let s be Element of S; :: thesis: for BASSIGN being non empty Subset of (ModelSP S)
for kai being Function of atomic_WFF, the BasicAssign of (BASSModel (R,BASSIGN)) holds
( s,kai |= EX H iff ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) )
let BASSIGN be non empty Subset of (ModelSP S); :: thesis: for kai being Function of atomic_WFF, the BasicAssign of (BASSModel (R,BASSIGN)) holds
( s,kai |= EX H iff ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) )
let kai be Function of atomic_WFF, the BasicAssign of (BASSModel (R,BASSIGN)); :: thesis: ( s,kai |= EX H iff ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) )
A1: ( ex pai being inf_path of R st
( pai . 0 = s & pai . 1 |= Evaluate (H,kai) ) implies ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) ) by Def60;
( s,kai |= EX H iff s |= EX (Evaluate (H,kai)) ) by Th7;
hence ( s,kai |= EX H iff ex pai being inf_path of R st
( pai . 0 = s & pai . 1,kai |= H ) ) by A1, Th14; :: thesis: verum