Nuprl Lemma : l_subset-l_contains
∀[T:Type]. ∀A,B:T List. (l_subset(T;A;B) ⇐⇒ A ⊆ B)
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
l_subset: l_subset(T;as;bs),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_contains: A ⊆ B,
l_subset: l_subset(T;as;bs),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
l_all_wf,
l_member_wf,
l_all_iff,
all_wf,
iff_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
because_Cache,
addLevel,
productElimination,
impliesFunctionality,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}A,B:T List. (l\_subset(T;A;B) \mLeftarrow{}{}\mRightarrow{} A \msubseteq{} B)
Date html generated:
2016_05_14-AM-07_53_35
Last ObjectModification:
2015_12_26-PM-04_47_36
Theory : list_1
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