Nuprl Lemma : append_is_nil_test
∀[a,b:Top List].
((([] = (a @ b) ∈ (Top List)) ∨ ((a @ b) = [] ∈ (Top List))) ⇒ ((b = [] ∈ (Top List)) ∧ (a = [] ∈ (Top List))))
Proof
Definitions occuring in Statement :
append: as @ bs,
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
or: P ∨ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
append_is_nil,
top_wf,
or_wf,
equal_wf,
list_wf,
nil_wf,
append_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
thin,
equalitySymmetry,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
productElimination,
independent_isectElimination,
independent_pairFormation,
because_Cache,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[a,b:Top List]. ((([] = (a @ b)) \mvee{} ((a @ b) = [])) {}\mRightarrow{} ((b = []) \mwedge{} (a = [])))
Date html generated:
2016_05_15-PM-03_21_38
Last ObjectModification:
2015_12_27-PM-01_04_25
Theory : general
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