let N be non empty with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated AMI-Struct over N

for P being Instruction-Sequence of S

for s being State of S

for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let S be non empty with_non-empty_values IC-Ins-separated AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S

for s being State of S

for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let P be Instruction-Sequence of S; :: thesis: for s being State of S

for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let s be State of S; :: thesis: for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let i be Instruction of S; :: thesis: (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

NAT = dom P by PARTFUN1:def 2;

hence (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s)) by PARTFUN1:def 6; :: thesis: verum

for P being Instruction-Sequence of S

for s being State of S

for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let S be non empty with_non-empty_values IC-Ins-separated AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S

for s being State of S

for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let P be Instruction-Sequence of S; :: thesis: for s being State of S

for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let s be State of S; :: thesis: for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

let i be Instruction of S; :: thesis: (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s))

NAT = dom P by PARTFUN1:def 2;

hence (Exec ((P . (IC s)),s)) . (IC ) = IC (Following (P,s)) by PARTFUN1:def 6; :: thesis: verum