let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA

for I being really-closed MacroInstruction of SCM+FSA

for a being read-write Int-Location st s . a <= 0 holds

while>0 (a,I) is_halting_onInit s,P

let s be State of SCM+FSA; :: thesis: for I being really-closed MacroInstruction of SCM+FSA

for a being read-write Int-Location st s . a <= 0 holds

while>0 (a,I) is_halting_onInit s,P

let I be really-closed MacroInstruction of SCM+FSA ; :: thesis: for a being read-write Int-Location st s . a <= 0 holds

while>0 (a,I) is_halting_onInit s,P

let a be read-write Int-Location; :: thesis: ( s . a <= 0 implies while>0 (a,I) is_halting_onInit s,P )

set s0 = Initialized s;

assume s . a <= 0 ; :: thesis: while>0 (a,I) is_halting_onInit s,P

then A1: (Initialized s) . a <= 0 by SCMFSA_M:37;

while>0 (a,I) is_halting_on Initialized s,P by A1, SCMFSA_9:38;

hence while>0 (a,I) is_halting_onInit s,P by Th27; :: thesis: verum

for I being really-closed MacroInstruction of SCM+FSA

for a being read-write Int-Location st s . a <= 0 holds

while>0 (a,I) is_halting_onInit s,P

let s be State of SCM+FSA; :: thesis: for I being really-closed MacroInstruction of SCM+FSA

for a being read-write Int-Location st s . a <= 0 holds

while>0 (a,I) is_halting_onInit s,P

let I be really-closed MacroInstruction of SCM+FSA ; :: thesis: for a being read-write Int-Location st s . a <= 0 holds

while>0 (a,I) is_halting_onInit s,P

let a be read-write Int-Location; :: thesis: ( s . a <= 0 implies while>0 (a,I) is_halting_onInit s,P )

set s0 = Initialized s;

assume s . a <= 0 ; :: thesis: while>0 (a,I) is_halting_onInit s,P

then A1: (Initialized s) . a <= 0 by SCMFSA_M:37;

while>0 (a,I) is_halting_on Initialized s,P by A1, SCMFSA_9:38;

hence while>0 (a,I) is_halting_onInit s,P by Th27; :: thesis: verum