Nuprl Lemma : fset-add_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[s:fset(T)]. ∀[x:T]. (fset-add(eq;x;s) ∈ fset(T))
Proof
Definitions occuring in Statement :
fset-add: fset-add(eq;x;s),
fset: fset(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
fset-add: fset-add(eq;x;s),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
fset-union_wf,
fset-singleton_wf,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
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{}[s:fset(T)]. \mforall{}[x:T]. (fset-add(eq;x;s) \mmember{} fset(T))
Date html generated:
2016_05_14-PM-03_39_47
Last ObjectModification:
2015_12_26-PM-06_41_29
Theory : finite!sets
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