let z be natural number ; :: thesis: for N being non empty with_non-empty_elements set
for T being non empty stored-program IC-Ins-separated definite standard AMI-Struct of N
for f, g being Element of NAT st f + z,T = g + z,T holds
f = g
let N be non empty with_non-empty_elements set ; :: thesis: for T being non empty stored-program IC-Ins-separated definite standard AMI-Struct of N
for f, g being Element of NAT st f + z,T = g + z,T holds
f = g
let T be non empty stored-program IC-Ins-separated definite standard AMI-Struct of N; :: thesis: for f, g being Element of NAT st f + z,T = g + z,T holds
f = g
let f, g be Element of NAT ; :: thesis: ( f + z,T = g + z,T implies f = g )
assume f + z,T = g + z,T ; :: thesis: f = g
then (locnum f,T) + z = (locnum g,T) + z by Th25;
hence f = g by Th27; :: thesis: verum