Nuprl Lemma : bag-decomp_wf2
∀[T:Type]. ∀[bs:bag(T)]. (bag-decomp(bs) ∈ bag({p:T × bag(T)| bs = ({fst(p)} + (snd(p))) ∈ bag(T)} ))
Proof
Definitions occuring in Statement :
bag-decomp: bag-decomp(bs),
bag-append: as + bs,
single-bag: {x},
bag: bag(T),
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
member: t ∈ T,
set: {x:A| B[x]} ,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
pi1: fst(t),
pi2: snd(t),
squash: ↓T,
true: True
Lemmas referenced :
true_wf,
squash_wf,
and_wf,
bag-member-decomp,
bag-member_wf,
pi2_wf,
pi1_wf,
single-bag_wf,
bag-append_wf,
equal_wf,
bag-decomp_wf,
bag_wf,
bag-settype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_isectElimination,
lambdaFormation,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality,
productElimination,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
setElimination,
rename,
setEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[T:Type]. \mforall{}[bs:bag(T)]. (bag-decomp(bs) \mmember{} bag(\{p:T \mtimes{} bag(T)| bs = (\{fst(p)\} + (snd(p)))\} ))
Date html generated:
2016_05_15-PM-02_55_05
Last ObjectModification:
2016_01_16-AM-08_39_58
Theory : bags
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