Nuprl Lemma : sublist_interleaved
∀[T:Type]. ∀L,L1:T List. (L1 ⊆ L ⇒ (∃L2:T List. interleaving(T;L1;L2;L)))
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
or: P ∨ Q
Lemmas referenced :
list_induction,
all_wf,
list_wf,
sublist_wf,
exists_wf,
interleaving_wf,
istype-universe,
nil_wf,
sublist_nil,
interleaving_of_nil,
cons_wf,
nil_interleaving,
cons_sublist_cons,
cons_interleaving,
cons_interleaving2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
hypothesis,
functionEquality,
because_Cache,
inhabitedIsType,
universeIsType,
independent_functionElimination,
rename,
functionIsType,
productIsType,
dependent_functionElimination,
universeEquality,
dependent_pairFormation_alt,
productElimination,
independent_pairFormation,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
unionElimination
Latex:
\mforall{}[T:Type]. \mforall{}L,L1:T List. (L1 \msubseteq{} L {}\mRightarrow{} (\mexists{}L2:T List. interleaving(T;L1;L2;L)))
Date html generated:
2019_10_15-AM-10_56_56
Last ObjectModification:
2018_10_09-AM-10_07_19
Theory : list!
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