Nuprl Lemma : decidable__f-subset
∀[T:Type]. ∀eq:EqDecider(T). ∀xs,ys:fset(T). Dec(xs ⊆ ys)
Proof
Definitions occuring in Statement :
f-subset: xs ⊆ ys,
fset: fset(T),
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
f-subset: xs ⊆ ys,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
decidable__all_fset,
fset-member_wf,
decidable__fset-member,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}xs,ys:fset(T). Dec(xs \msubseteq{} ys)
Date html generated:
2016_05_14-PM-03_41_29
Last ObjectModification:
2015_12_26-PM-06_40_22
Theory : finite!sets
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