Nuprl Lemma : adjacent-to-same-sublist2
∀[T:Type]
∀L1,L2:T List. ∀a,b,c:T.
L1 ⊆ L2 ⇒ adjacent(T;L1;a;b) ⇒ adjacent(T;L2;a;c) ⇒ (c before b ∈ L2 ∨ (b = c ∈ T)) supposing no_repeats(T;L2)
Proof
Definitions occuring in Statement :
adjacent: adjacent(T;L;x;y),
l_before: x before y ∈ l,
sublist: L1 ⊆ L2,
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
no_repeats_witness,
adjacent-sublist,
before-adjacent2,
adjacent_wf,
sublist_wf,
no_repeats_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
rename,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}L1,L2:T List. \mforall{}a,b,c:T.
L1 \msubseteq{} L2 {}\mRightarrow{} adjacent(T;L1;a;b) {}\mRightarrow{} adjacent(T;L2;a;c) {}\mRightarrow{} (c before b \mmember{} L2 \mvee{} (b = c))
supposing no\_repeats(T;L2)
Date html generated:
2016_05_15-PM-03_42_03
Last ObjectModification:
2015_12_27-PM-01_18_12
Theory : general
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