let n be Element of NAT ; :: thesis: for X being set
for A being Subset of X
for A1 being SetSequence of X holds (inferior_setsequence (A (/\) A1)) . n = A /\ ((inferior_setsequence A1) . n)
let X be set ; :: thesis: for A being Subset of X
for A1 being SetSequence of X holds (inferior_setsequence (A (/\) A1)) . n = A /\ ((inferior_setsequence A1) . n)
let A be Subset of X; :: thesis: for A1 being SetSequence of X holds (inferior_setsequence (A (/\) A1)) . n = A /\ ((inferior_setsequence A1) . n)
let A1 be SetSequence of X; :: thesis: (inferior_setsequence (A (/\) A1)) . n = A /\ ((inferior_setsequence A1) . n)
(inferior_setsequence (A (/\) A1)) . n = Intersection ((A (/\) A1) ^\ n) by Th1
.= Intersection (A (/\) (A1 ^\ n)) by Th16
.= A /\ (Intersection (A1 ^\ n)) by Th33
.= A /\ ((inferior_setsequence A1) . n) by Th1 ;
hence (inferior_setsequence (A (/\) A1)) . n = A /\ ((inferior_setsequence A1) . n) ; :: thesis: verum