reserve x,y,z for object,
  i,j,n,m for Nat,
  D for non empty set,
  s,t for FinSequence,
  a,a1,a2,b1,b2,d for Element of D,
  p, p1,p2,q,r for FinSequence of D;
reserve M,M1,M2 for Matrix of D;
reserve f for FinSequence of D;
reserve i,j,i1,j1 for Nat;
reserve k for Nat, G for Matrix of D;
reserve x,y,x1,x2,y1,y2 for object,
  i,j,k,l,n,m for Nat,
  D for non empty set,
  s,s2 for FinSequence,
  a,b,c,d for Element of D,
  q,r for FinSequence of D,
  a9,b9 for Element of D;

theorem Th47:
  len (x1,x2)][(y1,y2)=2 & width (x1,x2)][(y1,y2)=2 & Indices (x1,
  x2)][(y1,y2)=[:Seg 2,Seg 2:]
proof
  set M = (x1,x2)][(y1,y2);
  thus
A1: len M=2 by FINSEQ_1:44;
  rng M = { <*x1,x2*>,<*y1,y2*>} by FINSEQ_2:127;
  then
A2: <*x1,x2*> in rng M by TARSKI:def 2;
  len <*x1,x2*>=2 by FINSEQ_1:44;
  hence width M=2 by A1,A2,Def3;
  hence thesis by A1,FINSEQ_1:def 3;
end;
