Nuprl Lemma : decidable__equal_bag
∀[T:Type]. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ (∀xs,ys:bag(T). Dec(xs = ys ∈ bag(T))))
Proof
Definitions occuring in Statement :
bag: bag(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q)
Lemmas referenced :
bag_wf,
all_wf,
decidable_wf,
equal_wf,
deq-exists,
assert-bag-eq,
assert_wf,
bag-eq_wf,
decidable__assert,
decidable_functionality,
iff_weakening_uiff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
universeEquality,
productElimination,
independent_functionElimination,
rename,
dependent_functionElimination,
independent_pairFormation
Latex:
\mforall{}[T:Type]. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} (\mforall{}xs,ys:bag(T). Dec(xs = ys)))
Date html generated:
2016_05_15-PM-08_00_40
Last ObjectModification:
2015_12_27-PM-04_15_55
Theory : bags_2
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