Nuprl Lemma : void-list-equality3
∀[x,y:Void List]. {(↑null(x)) ∧ (↑null(y))} supposing x = y ∈ (Void List)
Proof
Definitions occuring in Statement :
null: null(as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
and: P ∧ Q,
void: Void,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
guard: {T},
and: P ∧ Q,
subtype_rel: A ⊆r B,
top: Top,
so_apply: x[s],
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cand: A c∧ B,
true: True,
all: ∀x:A. B[x],
bfalse: ff
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
equal_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
equal-wf-base-T,
nil_wf,
null_nil_lemma,
equal-wf-base,
null_cons_lemma,
assert_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
voidEquality,
hypothesis,
hypothesisEquality,
productEquality,
applyEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
independent_functionElimination,
baseClosed,
natural_numberEquality,
independent_pairFormation,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
dependent_functionElimination
Latex:
\mforall{}[x,y:Void List]. \{(\muparrow{}null(x)) \mwedge{} (\muparrow{}null(y))\} supposing x = y
Date html generated:
2018_05_21-PM-07_36_04
Last ObjectModification:
2017_07_26-PM-05_10_10
Theory : general
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