Nuprl Lemma : fset_mem_wf
∀[T:Type]. ∀[x:T]. ∀[s:fset(T)]. (x ↓∈ s ∈ ℙ)
Proof
Definitions occuring in Statement :
fset_mem: x ↓∈ s,
fset: fset(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,
fset_mem: x ↓∈ s,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
squash_wf,
exists_wf,
list_wf,
and_wf,
equal_wf,
fset_wf,
list_subtype_fset,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[s:fset(T)]. (x \mdownarrow{}\mmember{} s \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_38_03
Last ObjectModification:
2015_12_26-PM-06_42_18
Theory : finite!sets
Home
Index