let n be Nat; :: thesis: for N being with_zero set
for S being non empty with_non-empty_values IC-Ins-separated standard AMI-Struct over N
for F being Subset of NAT st F = {n} holds
LocSeq (F,S) = 0 .--> n

let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated standard AMI-Struct over N
for F being Subset of NAT st F = {n} holds
LocSeq (F,S) = 0 .--> n

let S be non empty with_non-empty_values IC-Ins-separated standard AMI-Struct over N; :: thesis: for F being Subset of NAT st F = {n} holds
LocSeq (F,S) = 0 .--> n

let F be Subset of NAT; :: thesis: ( F = {n} implies LocSeq (F,S) = 0 .--> n )
assume A1: F = {n} ; :: thesis: LocSeq (F,S) = 0 .--> n
then A2: card F = by ;
{n} c= omega by ORDINAL1:def 12;
then A3: (canonical_isomorphism_of ((),())) . 0 = () . 0 by CARD_5:38
.= n by FUNCOP_1:72 ;
A4: dom (LocSeq (F,S)) = card F by Def1;
A5: for a being object st a in dom (LocSeq (F,S)) holds
(LocSeq (F,S)) . a = () . a
proof
let a be object ; :: thesis: ( a in dom (LocSeq (F,S)) implies (LocSeq (F,S)) . a = () . a )
assume A6: a in dom (LocSeq (F,S)) ; :: thesis: (LocSeq (F,S)) . a = () . a
then A7: a = 0 by ;
thus (LocSeq (F,S)) . a = (canonical_isomorphism_of ((RelIncl ()),())) . a by A4, A6, Def1
.= () . a by ; :: thesis: verum
end;
thus LocSeq (F,S) = 0 .--> n by ; :: thesis: verum