Nuprl Lemma : nc-s_wf
∀[I,J:fset(ℕ)]. s ∈ I ⟶ J supposing J ⊆ I
Proof
Definitions occuring in Statement :
nc-s: s,
names-hom: I ⟶ J,
f-subset: xs ⊆ ys,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
names-hom: I ⟶ J,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nc-s: s,
subtype_rel: A ⊆r B,
prop: ℙ,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
dM_inc_wf,
names-subtype,
names_wf,
f-subset_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
independent_isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
because_Cache,
natural_numberEquality,
isect_memberEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. s \mmember{} I {}\mrightarrow{} J supposing J \msubseteq{} I
Date html generated:
2016_05_18-PM-00_00_32
Last ObjectModification:
2015_12_28-PM-03_06_06
Theory : cubical!type!theory
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