Nuprl Lemma : tl_sublist
∀[T:Type]. ∀a:T. ∀L1,L2:T List. ([a / L1] ⊆ L2 ⇒ L1 ⊆ L2)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
cons: [a / b],
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,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
sublist_transitivity,
cons_wf,
sublist_tl,
null_cons_lemma,
istype-void,
reduce_tl_cons_lemma,
sublist_weakening,
sublist_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
independent_functionElimination,
because_Cache,
independent_isectElimination,
sqequalRule,
Error :memTop,
voidElimination,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}a:T. \mforall{}L1,L2:T List. ([a / L1] \msubseteq{} L2 {}\mRightarrow{} L1 \msubseteq{} L2)
Date html generated:
2020_05_20-AM-08_07_07
Last ObjectModification:
2020_01_28-PM-04_19_24
Theory : general
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