Nuprl Lemma : poset_properties
∀[s:POSet{i}]. UniformlyAntiSym(|s|;a,b.a ≤ b)
Proof
Definitions occuring in Statement :
poset: POSet{i},
set_leq: a ≤ b,
set_car: |p|,
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
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],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
poset_wf,
set_leq_wf,
set_car_wf,
sq_stable__uanti_sym
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[s:POSet\{i\}]. UniformlyAntiSym(|s|;a,b.a \mleq{} b)
Date html generated:
2016_05_15-PM-00_05_04
Last ObjectModification:
2016_01_15-AM-07_08_46
Theory : sets_1
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