Nuprl Lemma : fl-filter-filter
∀[P,Q,s:Top]. (fl-filter(fl-filter(s;x.P[x]);x.Q[x]) ~ fl-filter(s;x.P[x] ∧b Q[x]))
Proof
Definitions occuring in Statement :
fl-filter: fl-filter(s;x.Q[x]),
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fl-filter: fl-filter(s;x.Q[x]),
cal-filter: cal-filter(s;x.P[x]),
fset-filter: {x ∈ s | P[x]},
top: Top
Lemmas referenced :
top_wf,
filter-filter
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[P,Q,s:Top]. (fl-filter(fl-filter(s;x.P[x]);x.Q[x]) \msim{} fl-filter(s;x.P[x] \mwedge{}\msubb{} Q[x]))
Date html generated:
2016_05_18-AM-11_40_50
Last ObjectModification:
2016_01_15-PM-05_52_25
Theory : lattices
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