Nuprl Lemma : append_cancel_nil
∀[A:Type]. ∀[as,bs:A List]. bs = [] ∈ (A List) supposing as = (as @ bs) ∈ (A List)
Proof
Definitions occuring in Statement :
append: as @ bs,
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
append_cancel,
nil_wf,
equal_wf,
list_wf,
append_wf,
append-nil,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
applyEquality,
lambdaEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[A:Type]. \mforall{}[as,bs:A List]. bs = [] supposing as = (as @ bs)
Date html generated:
2016_05_14-PM-02_21_33
Last ObjectModification:
2015_12_26-PM-04_27_41
Theory : list_1
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