Nuprl Lemma : adjacent-sublist
∀[T:Type]. ∀L1,L2:T List. (L1 ⊆ L2 ⇒ (∀x,y:T. (adjacent(T;L1;x;y) ⇒ x before y ∈ L2)))
Proof
Definitions occuring in Statement :
adjacent: adjacent(T;L;x;y),
l_before: x before y ∈ l,
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ
Lemmas referenced :
l_before_sublist,
adjacent-before,
adjacent_wf,
sublist_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
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. (L1 \msubseteq{} L2 {}\mRightarrow{} (\mforall{}x,y:T. (adjacent(T;L1;x;y) {}\mRightarrow{} x before y \mmember{} L2)))
Date html generated:
2016_05_15-PM-03_41_26
Last ObjectModification:
2015_12_27-PM-01_17_45
Theory : general
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