Nuprl Lemma : permr_nil_is_nil
∀T:Type. ∀as:T List. ((as ≡(T) []) ⇒ (as = [] ∈ (T List)))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
nil: [],
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
cons: [a / b],
implies: P ⇒ Q,
prop: ℙ,
false: False,
not: ¬A
Lemmas referenced :
list-cases,
product_subtype_list,
list_wf,
nil_wf,
permr_wf,
cons_wf,
not_permr_cons_nil
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesisEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
sqequalRule,
universeIsType,
universeEquality,
voidElimination,
independent_functionElimination
Latex:
\mforall{}T:Type. \mforall{}as:T List. ((as \mequiv{}(T) []) {}\mRightarrow{} (as = []))
Date html generated:
2019_10_16-PM-01_00_23
Last ObjectModification:
2018_10_08-AM-10_29_26
Theory : perms_2
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