Nuprl Lemma : bag-splits_wf
∀T:Type. ∀b:bag(T). (bag-splits(b) ∈ bag(bag(T) × bag(T)))
Proof
Definitions occuring in Statement :
bag-splits: bag-splits(b),
bag: bag(T),
all: ∀x:A. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
bag: bag(T),
uall: ∀[x:A]. B[x],
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
bag_wf,
quotient-member-eq,
list_wf,
permutation_wf,
permutation-equiv,
bag-splits_wf_list,
bag-splits-permutation,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
lemma_by_obid,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}b:bag(T). (bag-splits(b) \mmember{} bag(bag(T) \mtimes{} bag(T)))
Date html generated:
2016_05_15-PM-02_53_16
Last ObjectModification:
2015_12_27-AM-09_32_00
Theory : bags
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