Nuprl Lemma : cons-bag_wf
∀[T:Type]. ∀[x:T]. ∀[b:bag(T)]. (x.b ∈ bag(T))
Proof
Definitions occuring in Statement :
cons-bag: x.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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
cons-bag: x.b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
top: Top,
prop: ℙ,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
list_wf,
quotient-member-eq,
permutation_wf,
permutation-equiv,
cons_wf,
permutation-cons,
nil_wf,
nil-append,
equal_wf,
append_wf,
length_wf,
length_of_cons_lemma,
list_ind_nil_lemma,
exists_wf,
length-append,
equal-wf-base,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
hypothesis,
equalitySymmetry,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaFormation,
rename,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
productEquality,
applyLambdaEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[b:bag(T)]. (x.b \mmember{} bag(T))
Date html generated:
2017_10_01-AM-08_44_56
Last ObjectModification:
2017_07_26-PM-04_30_26
Theory : bags
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