Nuprl Lemma : sqequal-null
∀[T:Type]. ∀[l:T List].  l ~ [] supposing ↑null(l)
Proof
Definitions occuring in Statement : 
null: null(as)
, 
nil: []
, 
list: T List
, 
assert: ↑b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
prop: ℙ
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
Lemmas referenced : 
sqequal-nil, 
assert_wf, 
null_wf, 
list_wf, 
assert_of_null
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
axiomSqEquality, 
Error :universeIsType, 
sqequalRule, 
Error :isect_memberEquality_alt, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
productElimination
Latex:
\mforall{}[T:Type].  \mforall{}[l:T  List].    l  \msim{}  []  supposing  \muparrow{}null(l)
Date html generated:
2019_06_20-PM-01_19_19
Last ObjectModification:
2018_09_30-PM-03_56_42
Theory : list_1
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