Nuprl Lemma : set_lt_irreflexivity
∀[s:QOSet]. ∀[a:|s|]. False supposing a <s a
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_lt: a <p b,
set_car: |p|,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
qoset: QOSet,
dset: DSet
Lemmas referenced :
qoset_lt_irrefl,
set_lt_wf,
set_car_wf,
qoset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
independent_isectElimination,
hypothesis,
independent_functionElimination,
voidElimination,
sqequalRule,
setElimination,
rename,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[s:QOSet]. \mforall{}[a:|s|]. False supposing a <s a
Date html generated:
2016_05_15-PM-00_04_49
Last ObjectModification:
2015_12_26-PM-11_28_02
Theory : sets_1
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