let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for p being PartState of S
for l being Element of NAT st l in dom p holds
l in dom (ProgramPart p)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S
for l being Element of NAT st l in dom p holds
l in dom (ProgramPart p)
let p be PartState of S; :: thesis: for l being Element of NAT st l in dom p holds
l in dom (ProgramPart p)
let l be Element of NAT ; :: thesis: ( l in dom p implies l in dom (ProgramPart p) )
A1: dom (ProgramPart p) = (dom p) /\ NAT by RELAT_1:90;
assume l in dom p ; :: thesis: l in dom (ProgramPart p)
hence l in dom (ProgramPart p) by A1, XBOOLE_0:def 4; :: thesis: verum