Nuprl Lemma : cons-not-nil
∀[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_neq_nil,
cons_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
voidElimination,
Error :equalityIsType3,
Error :inhabitedIsType,
baseClosed,
sqequalRule,
Error :lambdaEquality_alt,
dependent_functionElimination,
because_Cache,
Error :universeIsType,
Error :isect_memberEquality_alt,
universeEquality
Latex:
\mforall{}[S:Type]. \mforall{}[a:S]. \mforall{}[b:S List]. (\mneg{}([a / b] = []))
Date html generated:
2019_06_20-PM-00_40_26
Last ObjectModification:
2018_09_30-PM-11_01_37
Theory : list_0
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