theorem Th76: :: PRE_POLY:78

for X being set
for A being finite Subset of X
for a being Element of X st not a in A holds
for B being finite Subset of X st B = {a} \/ A holds
for R being Order of X st R linearly_orders B holds
for k being Element of NAT st k in dom (SgmX (R,B)) & (SgmX (R,B)) /. k = a holds
for i being Element of NAT st 1 <= i & i <= k - 1 holds
(SgmX (R,B)) /. i = (SgmX (R,A)) /. i