Nuprl Lemma : null_functionality_wrt_permr
∀T:Type. ∀as,bs:T List. ((as ≡(T) bs) ⇒ null(as) = null(bs))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
null: null(as),
list: T List,
bool: 𝔹,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
implies: P ⇒ Q,
prop: ℙ,
cons: [a / b],
top: Top,
not: ¬A,
false: False
Lemmas referenced :
list_wf,
list-cases,
null_nil_lemma,
btrue_wf,
permr_wf,
nil_wf,
product_subtype_list,
null_cons_lemma,
istype-void,
cons_wf,
bfalse_wf,
not_permr_cons_nil,
permr_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
inhabitedIsType,
hypothesisEquality,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
universeEquality,
dependent_functionElimination,
unionElimination,
sqequalRule,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality_alt,
voidElimination,
independent_functionElimination
Latex:
\mforall{}T:Type. \mforall{}as,bs:T List. ((as \mequiv{}(T) bs) {}\mRightarrow{} null(as) = null(bs))
Date html generated:
2019_10_16-PM-01_04_02
Last ObjectModification:
2018_10_08-AM-10_18_11
Theory : list_2
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