Nuprl Lemma : eval_bag_wf
∀[T:Type]. ∀[b:bag(T)]. (eval_bag(b) ∈ bag(T))
Proof
Definitions occuring in Statement :
eval_bag: eval_bag(b),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag: bag(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
eval_bag: eval_bag(b),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
bag_wf,
equal-wf-base,
list_wf,
permutation_wf,
quotient-member-eq,
permutation-equiv,
eval_list_wf,
eval_list_sq,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
productEquality,
cumulativity,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. (eval\_bag(b) \mmember{} bag(T))
Date html generated:
2016_05_15-PM-02_21_37
Last ObjectModification:
2015_12_27-AM-09_55_28
Theory : bags
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