Nuprl Lemma : names-subtype
∀[I,J:fset(ℕ)]. names(I) ⊆r names(J) supposing I ⊆ J
Proof
Definitions occuring in Statement :
names: names(I),
f-subset: xs ⊆ ys,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
names: names(I),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
f-subset: xs ⊆ ys
Lemmas referenced :
subtype_rel_sets,
nat_wf,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
f-subset_wf,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
lambdaEquality,
applyEquality,
intEquality,
independent_isectElimination,
natural_numberEquality,
hypothesisEquality,
setElimination,
rename,
setEquality,
lambdaFormation,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. names(I) \msubseteq{}r names(J) supposing I \msubseteq{} J
Date html generated:
2016_05_18-AM-11_56_15
Last ObjectModification:
2015_12_28-PM-03_09_01
Theory : cubical!type!theory
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