let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite AMI-Struct of N
for P being the Instructions of b₁ -valued ManySortedSet of NAT
for s being State of S
for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC S) = IC (Following (P,s))
let S be non empty stored-program IC-Ins-separated definite AMI-Struct of N; :: thesis: for P being the Instructions of S -valued ManySortedSet of NAT
for s being State of S
for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC S) = IC (Following (P,s))
let P be the Instructions of S -valued ManySortedSet of NAT ; :: thesis: for s being State of S
for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC S) = IC (Following (P,s))
let s be State of S; :: thesis: for i being Instruction of S holds (Exec ((P . (IC s)),s)) . (IC S) = IC (Following (P,s))
let i be Instruction of S; :: thesis: (Exec ((P . (IC s)),s)) . (IC S) = IC (Following (P,s))
NAT = dom P by PARTFUN1:def 4;
hence (Exec ((P . (IC s)),s)) . (IC S) = IC (Following (P,s)) by PARTFUN1:def 8; :: thesis: verum