let a be Int_position; :: thesis: for k1 being Integer
for I, J being Program of holds
( 0 in dom (if>0 (a,k1,I,J)) & 1 in dom (if>0 (a,k1,I,J)) )
let k1 be Integer; :: thesis: for I, J being Program of holds
( 0 in dom (if>0 (a,k1,I,J)) & 1 in dom (if>0 (a,k1,I,J)) )
let I, J be Program of ; :: thesis: ( 0 in dom (if>0 (a,k1,I,J)) & 1 in dom (if>0 (a,k1,I,J)) )
set ci = card (if>0 (a,k1,I,J));
card (if>0 (a,k1,I,J)) = ((card I) + (card J)) + 2 by Lm4;
then 2 <= card (if>0 (a,k1,I,J)) by NAT_1:12;
then 1 < card (if>0 (a,k1,I,J)) by XXREAL_0:2;
hence ( 0 in dom (if>0 (a,k1,I,J)) & 1 in dom (if>0 (a,k1,I,J)) ) by AFINSQ_1:66; :: thesis: verum