Nuprl Lemma : adjacent-member
∀[T:Type]. ∀L:T List. ∀x,y:T. (adjacent(T;L;x;y) ⇒ {(x ∈ L) ∧ (y ∈ L)})
Proof
Definitions occuring in Statement :
adjacent: adjacent(T;L;x;y),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
guard: {T},
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
adjacent-before,
l_before_member,
l_before_member2,
adjacent_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
universeEquality,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}x,y:T. (adjacent(T;L;x;y) {}\mRightarrow{} \{(x \mmember{} L) \mwedge{} (y \mmember{} L)\})
Date html generated:
2016_05_15-PM-03_41_21
Last ObjectModification:
2015_12_27-PM-01_17_41
Theory : general
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