Nuprl Lemma : listp-not-nil
∀[A:Type]. ∀[L:A List+]. (¬(L = [] ∈ (A List)))
Proof
Definitions occuring in Statement :
listp: A List+,
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
listp: A List+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
and: P ∧ Q,
cons: [a / b],
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
cons_neq_nil,
equal-wf-T-base,
list_wf,
less_than_wf,
length_wf,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
thin,
setElimination,
rename,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidEquality,
independent_functionElimination,
baseClosed,
because_Cache,
lambdaEquality,
Error :setIsType,
Error :universeIsType,
natural_numberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[L:A List\msupplus{}]. (\mneg{}(L = []))
Date html generated:
2019_06_20-PM-01_27_46
Last ObjectModification:
2018_09_26-PM-05_37_11
Theory : list_1
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