Nuprl Lemma : bag_all-map
∀[b,f,g:Top]. (bag_all(bag-map(g;b);f) ~ bag_all(b;f o g))
Proof
Definitions occuring in Statement :
bag_all: bag_all(b;f),
bag-map: bag-map(f;bs),
compose: f o g,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag_all: bag_all(b;f),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
compose: f o g,
so_apply: x[s]
Lemmas referenced :
bag-accum-map,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[b,f,g:Top]. (bag\_all(bag-map(g;b);f) \msim{} bag\_all(b;f o g))
Date html generated:
2016_05_15-PM-02_34_43
Last ObjectModification:
2015_12_27-AM-09_46_37
Theory : bags
Home
Index