let S be non empty set ; for BASSIGN being non empty Subset of (ModelSP (Inf_seq S))
for t being Element of Inf_seq S
for f being Assign of (Inf_seqModel (S,BASSIGN)) holds
( t |= 'X' f iff Shift (t,1) |= f )
let BASSIGN be non empty Subset of (ModelSP (Inf_seq S)); for t being Element of Inf_seq S
for f being Assign of (Inf_seqModel (S,BASSIGN)) holds
( t |= 'X' f iff Shift (t,1) |= f )
let t be Element of Inf_seq S; for f being Assign of (Inf_seqModel (S,BASSIGN)) holds
( t |= 'X' f iff Shift (t,1) |= f )
let f be Assign of (Inf_seqModel (S,BASSIGN)); ( t |= 'X' f iff Shift (t,1) |= f )
set S1 = Inf_seq S;
set t1 = Shift (t,1);
set t1p = Shift (t,1,S);
A1:
'X' f = Next_0 (f,S)
by Def48;
thus
( t |= 'X' f implies Shift (t,1) |= f )
( Shift (t,1) |= f implies t |= 'X' f )
assume
Shift (t,1) |= f
; t |= 'X' f
then
(Fid (f,(Inf_seq S))) . (Shift (t,1)) = TRUE
;
then
Next_univ (t,(Fid (f,(Inf_seq S)))) = TRUE
by Def46;
then
(Fid (('X' f),(Inf_seq S))) . t = TRUE
by A1, Def47;
hence
t |= 'X' f
; verum