Nuprl Lemma : non_neg_mset_size
∀s:DSet. ∀a:MSet{s}. (size{s}(a) ≥ 0 )
Proof
Definitions occuring in Statement :
mset_size: size{s}(a),
mset: MSet{s},
ge: i ≥ j ,
all: ∀x:A. B[x],
natural_number: $n,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
ge: i ≥ j ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
mset: MSet{s},
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
dset: DSet,
mset_size: size{s}(a),
squash: ↓T
Lemmas referenced :
sq_stable__le,
mset_size_wf,
squash_wf,
ge_wf,
list_wf,
set_car_wf,
non_neg_length,
permr_wf,
equal_wf,
equal-wf-base,
mset_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
pointwiseFunctionalityForEquality,
sqequalRule,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
because_Cache,
imageMemberEquality,
baseClosed,
productEquality
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. (size\{s\}(a) \mgeq{} 0 )
Date html generated:
2017_10_01-AM-09_59_31
Last ObjectModification:
2017_03_03-PM-01_00_36
Theory : mset
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