Nuprl Lemma : equal-nil-sq-nil
∀[T:Type]. ∀[L:T List].  L ~ [] supposing L = [] ∈ (T List)
Proof
Definitions occuring in Statement : 
nil: []
, 
list: T List
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
, 
sqequal: s ~ t
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
and: P ∧ Q
, 
prop: ℙ
Lemmas referenced : 
no-member-sq-nil, 
null_nil_lemma, 
btrue_wf, 
member-implies-null-eq-bfalse, 
and_wf, 
equal_wf, 
list_wf, 
null_wf, 
btrue_neq_bfalse, 
l_member_wf, 
nil_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
independent_isectElimination, 
lambdaFormation, 
sqequalRule, 
hypothesis, 
dependent_set_memberEquality, 
independent_pairFormation, 
equalityTransitivity, 
equalitySymmetry, 
applyEquality, 
lambdaEquality, 
setElimination, 
rename, 
productElimination, 
setEquality, 
independent_functionElimination, 
voidElimination, 
because_Cache, 
sqequalAxiom, 
isect_memberEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].    L  \msim{}  []  supposing  L  =  []
Date html generated:
2016_05_14-PM-02_50_08
Last ObjectModification:
2015_12_26-PM-02_36_31
Theory : list_1
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