Nuprl Lemma : assert-list-deq
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[as,bs:A List]. uiff(↑(list-deq(eq) as bs);as = bs ∈ (A List))
Proof
Definitions occuring in Statement :
list-deq: list-deq(eq),
list: T List,
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
deq: EqDecider(T),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list-deq_wf,
deq_wf,
list_wf,
assert_wf,
assert_witness,
equal_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaFormation,
setElimination,
rename,
independent_pairFormation,
isect_memberFormation,
applyEquality,
functionExtensionality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
because_Cache,
universeEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[as,bs:A List]. uiff(\muparrow{}(list-deq(eq) as bs);as = bs)
Date html generated:
2017_04_14-AM-08_55_28
Last ObjectModification:
2017_02_27-PM-03_39_18
Theory : omega
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