Nuprl Lemma : nil-not-cons
∀[S:Type]. ∀[a:S]. ∀[b:S List]. (¬([] = [a / b] ∈ (S List)))
Proof
Definitions occuring in Statement :
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
cons-not-nil,
cons_wf,
list_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :lambdaFormation_alt,
independent_functionElimination,
equalitySymmetry,
voidElimination,
Error :equalityIsType2,
Error :inhabitedIsType,
baseClosed,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[S:Type]. \mforall{}[a:S]. \mforall{}[b:S List]. (\mneg{}([] = [a / b]))
Date html generated:
2019_06_20-PM-00_40_29
Last ObjectModification:
2018_09_30-PM-11_06_48
Theory : list_0
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