Nuprl Lemma : fset-pair_wf
∀[T:Type]. ∀[a,b:T]. ({a,b} ∈ fset(T))
Proof
Definitions occuring in Statement :
fset-pair: {a,b},
fset: fset(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-pair: {a,b},
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
cons_wf,
nil_wf,
list_subtype_fset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:T]. (\{a,b\} \mmember{} fset(T))
Date html generated:
2016_05_14-PM-03_38_54
Last ObjectModification:
2015_12_26-PM-06_41_51
Theory : finite!sets
Home
Index