Nuprl Lemma : bag-map'_wf
∀[B,A:Type]. ∀[b:bag(A)]. ∀[f:{x:A| x ↓∈ b} ⟶ B]. (bag-map'(f;b) ∈ bag(B))
Proof
Definitions occuring in Statement :
bag-map': bag-map'(f;b),
bag-member: x ↓∈ bs,
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
exists: ∃x:A. B[x],
bag-map': bag-map'(f;b),
uimplies: b supposing a,
all: ∀x:A. B[x],
true: True,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
iff_weakening_equal,
member_wf,
subtype_rel_bag,
true_wf,
squash_wf,
all_wf,
bag-subtype,
list-subtype-bag,
bag-map_wf,
bag-eq-subtype,
bag_to_squash_list,
bag_wf,
bag-member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
functionEquality,
setEquality,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
universeEquality,
isect_memberFormation,
introduction,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
imageElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
lambdaFormation,
cumulativity,
applyEquality,
lambdaEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[B,A:Type]. \mforall{}[b:bag(A)]. \mforall{}[f:\{x:A| x \mdownarrow{}\mmember{} b\} {}\mrightarrow{} B]. (bag-map'(f;b) \mmember{} bag(B))
Date html generated:
2016_05_15-PM-07_58_33
Last ObjectModification:
2016_01_16-PM-01_30_17
Theory : bags_2
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