Nuprl Lemma : n-intersecting_wf
∀[A,T:Type]. ∀[n:ℤ]. (n-intersecting(A;T;n) ∈ ℙ) supposing T ⊆r (A List)
Proof
Definitions occuring in Statement :
n-intersecting: n-intersecting(A;T;n),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
n-intersecting: n-intersecting(A;T;n),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
list_wf,
equal-wf-T-base,
length_wf,
int_subtype_base,
exists_wf,
l_all_wf2,
l_member_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
intEquality,
applyEquality,
because_Cache,
lambdaFormation,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A,T:Type]. \mforall{}[n:\mBbbZ{}]. (n-intersecting(A;T;n) \mmember{} \mBbbP{}) supposing T \msubseteq{}r (A List)
Date html generated:
2016_05_15-PM-06_24_11
Last ObjectModification:
2015_12_27-PM-00_03_38
Theory : general
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