Nuprl Lemma : bag-map-single
∀[x,f:Top]. (bag-map(f;{x}) ~ {f x})
Proof
Definitions occuring in Statement :
bag-map: bag-map(f;bs),
single-bag: {x},
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
bag_map_single_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
isectElimination,
because_Cache
Latex:
\mforall{}[x,f:Top]. (bag-map(f;\{x\}) \msim{} \{f x\})
Date html generated:
2016_05_15-PM-02_25_43
Last ObjectModification:
2015_12_27-AM-09_52_45
Theory : bags
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