let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program halting IC-Ins-separated definite AMI-Struct of N
for p being NAT -defined the Instructions of b₁ -valued finite Function
for s being State of S st ex k being Element of NAT st p halts_at IC (Comput p,s,k) holds
for i being Nat holds Result p,s = Result p,(Comput p,s,i)
let S be non empty stored-program halting IC-Ins-separated definite AMI-Struct of N; :: thesis: for p being NAT -defined the Instructions of S -valued finite Function
for s being State of S st ex k being Element of NAT st p halts_at IC (Comput p,s,k) holds
for i being Nat holds Result p,s = Result p,(Comput p,s,i)
let p be NAT -defined the Instructions of S -valued finite Function; :: thesis: for s being State of S st ex k being Element of NAT st p halts_at IC (Comput p,s,k) holds
for i being Nat holds Result p,s = Result p,(Comput p,s,i)
let s be State of S; :: thesis: ( ex k being Element of NAT st p halts_at IC (Comput p,s,k) implies for i being Nat holds Result p,s = Result p,(Comput p,s,i) )
given k being Element of NAT such that A1: p halts_at IC (Comput p,s,k) ; :: thesis: for i being Nat holds Result p,s = Result p,(Comput p,s,i)
A2: IC (Comput p,s,k) in dom p by A1, Def15;
let i be Nat; :: thesis: Result p,s = Result p,(Comput p,s,i)
p . (IC (Comput p,s,k)) = halt S by A1, Def15;
hence Result p,s = Result p,(Comput p,s,i) by A2, Th57; :: thesis: verum