reserve IIG for monotonic Circuit-like non void non empty ManySortedSign;
reserve SCS for non-empty Circuit of IIG;
reserve s for State of SCS;
reserve iv for InputValues of SCS;
reserve IIG for finite monotonic Circuit-like non void non empty
  ManySortedSign;
reserve SCS for non-empty Circuit of IIG;
reserve InpFs for InputFuncs of SCS;
reserve s for State of SCS;
reserve iv for InputValues of SCS;

theorem Th17:
  commute InpFs is constant & InputVertices IIG is non empty & iv
= (commute InpFs).0 implies for s being State of SCS, v being Vertex of IIG, n
being Element of NAT st n = depth SCS holds ((Computation(s,InpFs)).n qua State
  of SCS).v = IGValue(v,iv)
proof
  assume
A1: commute InpFs is constant & InputVertices IIG is non empty & iv = (
  commute InpFs).0;
  let s be State of SCS, v be Vertex of IIG;
A2: depth(v,SCS) <= depth SCS by CIRCUIT1:17;
  let n be Element of NAT;
  assume n = depth SCS;
  hence thesis by A1,A2,Th16;
end;
