Nuprl Lemma : mset_mon_wf
∀s:DSet. (mset_mon{s} ∈ AbMon)
Proof
Definitions occuring in Statement :
mset_mon: mset_mon{s},
all: ∀x:A. B[x],
member: t ∈ T,
abmonoid: AbMon,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
mset_mon: mset_mon{s},
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
null_mset: 0{s},
mset_sum: a + b,
ident: Ident(T;op;id),
infix_ap: x f y,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
and: P ∧ Q,
mset: MSet{s},
quotient: x,y:A//B[x; y],
dset: DSet,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
dset_wf,
mk_abmonoid,
mset_wf,
eq_mset_wf,
btrue_wf,
mset_sum_wf,
null_mset_wf,
mset_sum_assoc,
mset_sum_comm,
list_ind_nil_lemma,
quotient-member-eq,
list_wf,
set_car_wf,
permr_wf,
permr_equiv_rel,
append_wf,
nil_wf,
append_back_nil,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
lambdaEquality,
independent_isectElimination,
because_Cache,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
introduction,
independent_pairFormation,
productElimination,
independent_pairEquality,
axiomEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productEquality
Latex:
\mforall{}s:DSet. (mset\_mon\{s\} \mmember{} AbMon)
Date html generated:
2016_05_16-AM-07_47_05
Last ObjectModification:
2015_12_28-PM-06_03_37
Theory : mset
Home
Index