Nuprl Lemma : f-proper-subset_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[xs,ys:fset(T)]. (xs ⊆≠ ys ∈ ℙ)
Proof
Definitions occuring in Statement :
f-proper-subset: xs ⊆≠ ys,
fset: fset(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
f-proper-subset: xs ⊆≠ ys
Lemmas referenced :
and_wf,
f-subset_wf,
not_wf,
equal_wf,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[xs,ys:fset(T)]. (xs \msubseteq{}\mneq{} ys \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_41_52
Last ObjectModification:
2015_12_26-PM-06_40_05
Theory : finite!sets
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