let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite standard AMI-Struct of N
for F being NAT -defined lower FinPartState of
for f being Element of NAT st f in dom F holds
locnum f,S < card F
let S be non empty stored-program IC-Ins-separated definite standard AMI-Struct of N; :: thesis: for F being NAT -defined lower FinPartState of
for f being Element of NAT st f in dom F holds
locnum f,S < card F
let F be NAT -defined lower FinPartState of ; :: thesis: for f being Element of NAT st f in dom F holds
locnum f,S < card F
let f be Element of NAT ; :: thesis: ( f in dom F implies locnum f,S < card F )
assume A1: f in dom F ; :: thesis: locnum f,S < card F
f = il. S,(locnum f,S) by AMISTD_1:def 13;
hence locnum f,S < card F by A1, AMISTD_1:50; :: thesis: verum