Nuprl Lemma : loset_properties
∀s:LOSet. Connex(|s|;x,y.x ≤ y)
Proof
Definitions occuring in Statement :
loset: LOSet,
set_leq: a ≤ b,
set_car: |p|,
connex: Connex(T;x,y.R[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
loset: LOSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
loset_wf,
decidable__set_leq,
set_leq_wf,
set_car_wf,
sq_stable__connex
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
introduction,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}s:LOSet. Connex(|s|;x,y.x \mleq{} y)
Date html generated:
2016_05_15-PM-00_05_22
Last ObjectModification:
2016_01_15-AM-07_08_47
Theory : sets_1
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