Nuprl Lemma : mk_mset_cons
∀s:DSet. ∀a:|s|. ∀as:|s| List. (mk_mset([a / as]) = (mset_inj{s}(a) + mk_mset(as)) ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_sum: a + b,
mset_inj: mset_inj{s}(x),
mk_mset: mk_mset(as),
mset: MSet{s},
cons: [a / b],
list: T List,
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
mk_mset: mk_mset(as),
mset_inj: mset_inj{s}(x),
mset_sum: a + b,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_wf,
set_car_wf,
dset_wf,
mset_sum_wf,
mset_inj_wf,
mk_mset_wf,
list_ind_cons_lemma,
list_ind_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}s:DSet. \mforall{}a:|s|. \mforall{}as:|s| List. (mk\_mset([a / as]) = (mset\_inj\{s\}(a) + mk\_mset(as)))
Date html generated:
2016_05_16-AM-07_46_50
Last ObjectModification:
2015_12_28-PM-06_03_39
Theory : mset
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