let s be State of SCM+FSA; :: thesis: for a being read-write Int-Location
for bb, cc being Int-Location
for I being MacroInstruction of SCM+FSA
for p being Instruction-Sequence of SCM+FSA st s . (intloc 0) = 1 holds
((StepForUp (a,bb,cc,I,p,s)) . 0) . (intloc 0) = 1
let a be read-write Int-Location; :: thesis: for bb, cc being Int-Location
for I being MacroInstruction of SCM+FSA
for p being Instruction-Sequence of SCM+FSA st s . (intloc 0) = 1 holds
((StepForUp (a,bb,cc,I,p,s)) . 0) . (intloc 0) = 1
let bb, cc be Int-Location; :: thesis: for I being MacroInstruction of SCM+FSA
for p being Instruction-Sequence of SCM+FSA st s . (intloc 0) = 1 holds
((StepForUp (a,bb,cc,I,p,s)) . 0) . (intloc 0) = 1
let I be MacroInstruction of SCM+FSA ; :: thesis: for p being Instruction-Sequence of SCM+FSA st s . (intloc 0) = 1 holds
((StepForUp (a,bb,cc,I,p,s)) . 0) . (intloc 0) = 1
let p be Instruction-Sequence of SCM+FSA; :: thesis: ( s . (intloc 0) = 1 implies ((StepForUp (a,bb,cc,I,p,s)) . 0) . (intloc 0) = 1 )
set aux = 1 -stRWNotIn ({a,bb,cc} \/ (UsedILoc I));
set S = (s +* ((1 -stRWNotIn ({a,bb,cc} \/ (UsedILoc I))),(((s . cc) - (s . bb)) + 1))) +* (a,(s . bb));
A1: ((s +* ((1 -stRWNotIn ({a,bb,cc} \/ (UsedILoc I))),(((s . cc) - (s . bb)) + 1))) +* (a,(s . bb))) . (intloc 0) = (s +* ((1 -stRWNotIn ({a,bb,cc} \/ (UsedILoc I))),(((s . cc) - (s . bb)) + 1))) . (intloc 0) by FUNCT_7:32
.= s . (intloc 0) by FUNCT_7:32 ;
assume s . (intloc 0) = 1 ; :: thesis: ((StepForUp (a,bb,cc,I,p,s)) . 0) . (intloc 0) = 1
hence ((StepForUp (a,bb,cc,I,p,s)) . 0) . (intloc 0) = 1 by A1, SCMFSA_9:def 5; :: thesis: verum