let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated AMI-Struct of N
for p being NAT -defined the Instructions of b₁ -valued finite Function
for s being State of
for k being Nat holds Comput p,s,(k + 1) = Following p,(Comput p,s,k)
let S be non empty IC-Ins-separated AMI-Struct of N; :: thesis: for p being NAT -defined the Instructions of S -valued finite Function
for s being State of
for k being Nat holds Comput p,s,(k + 1) = Following p,(Comput p,s,k)
let p be NAT -defined the Instructions of S -valued finite Function; :: thesis: for s being State of
for k being Nat holds Comput p,s,(k + 1) = Following p,(Comput p,s,k)
let s be State of ; :: thesis: for k being Nat holds Comput p,s,(k + 1) = Following p,(Comput p,s,k)
let k be Nat; :: thesis: Comput p,s,(k + 1) = Following p,(Comput p,s,k)
deffunc H₁( set , State of ) -> State of = Following p,$2;
consider f being Function of NAT , product the Object-Kind of S such that
A1: Comput p,s,(k + 1) = f . (k + 1) and
A2: f . 0 = s and
A3: for i being Nat holds f . (i + 1) = H₁(i,f . i) by Def6;
consider g being Function of NAT , product the Object-Kind of S such that
A4: Comput p,s,k = g . k and
A5: g . 0 = s and
A6: for i being Nat holds g . (i + 1) = H₁(i,g . i) by Def6;
f = g from NAT_1:sch 16(A2, A3, A5, A6);
hence Comput p,s,(k + 1) = Following p,(Comput p,s,k) by A1, A4, A6; :: thesis: verum