Nuprl Lemma : member-nameset-diff
∀[L,X:Cname List]. ∀[x:nameset(L)]. x ∈ nameset(L-X) supposing ¬(x ∈ X)
Proof
Definitions occuring in Statement :
nameset: nameset(L),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
nameset: nameset(L),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cand: A c∧ B
Lemmas referenced :
not_wf,
l_member_wf,
coordinate_name_wf,
nameset_wf,
list_wf,
list-diff_wf,
cname_deq_wf,
member-list-diff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
because_Cache,
dependent_set_memberEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_pairFormation
Latex:
\mforall{}[L,X:Cname List]. \mforall{}[x:nameset(L)]. x \mmember{} nameset(L-X) supposing \mneg{}(x \mmember{} X)
Date html generated:
2016_05_20-AM-09_28_11
Last ObjectModification:
2015_12_28-PM-04_48_35
Theory : cubical!sets
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