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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