Nuprl Lemma : bag-deq_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. (bag-deq(eq) ∈ EqDecider(bag(T)))
Proof
Definitions occuring in Statement :
bag-deq: bag-deq(eq),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-deq: bag-deq(eq),
deq: EqDecider(T),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
bag-eq_wf,
bag_wf,
equal_wf,
assert-bag-eq,
assert_wf,
all_wf,
iff_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
independent_pairFormation,
because_Cache,
addLevel,
allFunctionality,
productElimination,
impliesFunctionality,
independent_isectElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. (bag-deq(eq) \mmember{} EqDecider(bag(T)))
Date html generated:
2016_05_15-PM-08_00_43
Last ObjectModification:
2015_12_27-PM-04_15_57
Theory : bags_2
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