Nuprl Lemma : l_contains_singleton
∀[T:Type]. ∀L:T List. ∀a:T. ([a] ⊆ L ⇐⇒ (a ∈ L))
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
l_member: (x ∈ l),
cons: [a / b],
nil: [],
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],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
and_wf,
l_member_wf,
l_contains_wf,
nil_wf,
l_contains_nil,
l_contains_cons,
cons_wf,
iff_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
addLevel,
impliesFunctionality,
because_Cache,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}a:T. ([a] \msubseteq{} L \mLeftarrow{}{}\mRightarrow{} (a \mmember{} L))
Date html generated:
2016_05_14-AM-07_54_43
Last ObjectModification:
2015_12_26-PM-04_48_57
Theory : list_1
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