let s be State of SCM+FSA ; :: thesis: for a being read-write Int-Location
for bb, cc being Int-Location
for I being Program of SCM+FSA st s . (intloc 0 ) = 1 holds
((StepForUp a,bb,cc,I,s) . 0 ) . (intloc 0 ) = 1
let a be read-write Int-Location ; :: thesis: for bb, cc being Int-Location
for I being Program of SCM+FSA st s . (intloc 0 ) = 1 holds
((StepForUp a,bb,cc,I,s) . 0 ) . (intloc 0 ) = 1
let bb, cc be Int-Location ; :: thesis: for I being Program of SCM+FSA st s . (intloc 0 ) = 1 holds
((StepForUp a,bb,cc,I,s) . 0 ) . (intloc 0 ) = 1
let I be Program of SCM+FSA ; :: thesis: ( s . (intloc 0 ) = 1 implies ((StepForUp a,bb,cc,I,s) . 0 ) . (intloc 0 ) = 1 )
set aux = 1 -stRWNotIn ({a,bb,cc} \/ (UsedIntLoc I));
set S = (s +* (1 -stRWNotIn ({a,bb,cc} \/ (UsedIntLoc I))),(((s . cc) - (s . bb)) + 1)) +* a,(s . bb);
A1: ((s +* (1 -stRWNotIn ({a,bb,cc} \/ (UsedIntLoc I))),(((s . cc) - (s . bb)) + 1)) +* a,(s . bb)) . (intloc 0 ) = (s +* (1 -stRWNotIn ({a,bb,cc} \/ (UsedIntLoc I))),(((s . cc) - (s . bb)) + 1)) . (intloc 0 ) by FUNCT_7:34
.= s . (intloc 0 ) by FUNCT_7:34 ;
assume s . (intloc 0 ) = 1 ; :: thesis: ((StepForUp a,bb,cc,I,s) . 0 ) . (intloc 0 ) = 1
hence ((StepForUp a,bb,cc,I,s) . 0 ) . (intloc 0 ) = 1 by A1, SCMFSA_9:def 5; :: thesis: verum