Nuprl Lemma : fset_map_wf
∀s,s':DSet. ∀f:|s| ⟶ |s'|. ∀a:MSet{s}. (fs-map(f, a) ∈ FiniteSet{s'})
Proof
Definitions occuring in Statement :
fset_map: fs-map(f, a),
finite_set: FiniteSet{s},
mset: MSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
fset_map: fs-map(f, a),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet
Lemmas referenced :
fset_of_mset_wf2,
mset_map_wf,
mset_wf,
set_car_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
functionEquality,
isectElimination,
setElimination,
rename
Latex:
\mforall{}s,s':DSet. \mforall{}f:|s| {}\mrightarrow{} |s'|. \mforall{}a:MSet\{s\}. (fs-map(f, a) \mmember{} FiniteSet\{s'\})
Date html generated:
2016_05_16-AM-07_50_29
Last ObjectModification:
2015_12_28-PM-06_00_46
Theory : mset
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