Nuprl Lemma : nil_sublist
∀[T:Type]. ∀L:T List. ([] ⊆ L ⇐⇒ True)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
true: True,
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,
true: True,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
sublist_wf,
nil_wf,
nil-sublist,
true_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. ([] \msubseteq{} L \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_14-AM-07_43_17
Last ObjectModification:
2015_12_26-PM-02_52_08
Theory : list_1
Home
Index