Nuprl Lemma : tl_wf
∀[A:Type]. ∀[l:A List]. (tl(l) ∈ A List)
Proof
Definitions occuring in Statement :
tl: tl(l),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
or: P ∨ Q,
cons: [a / b],
top: Top
Lemmas referenced :
list-cases,
reduce_tl_nil_lemma,
nil_wf,
product_subtype_list,
reduce_tl_cons_lemma,
istype-void,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
sqequalRule,
promote_hyp,
hypothesis_subsumption,
productElimination,
Error :isect_memberEquality_alt,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[l:A List]. (tl(l) \mmember{} A List)
Date html generated:
2019_06_20-PM-00_38_39
Last ObjectModification:
2018_10_08-PM-04_45_43
Theory : list_0
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