Nuprl Lemma : mset_sum_ident_r
∀s:DSet. ∀a:MSet{s}. ((a + 0{s}) = a ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_sum: a + b,
null_mset: 0{s},
mset: MSet{s},
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
abmonoid: AbMon,
mon: Mon,
prop: ℙ,
comm: Comm(T;op),
monoid_p: IsMonoid(T;op;id),
and: P ∧ Q,
ident: Ident(T;op;id),
assoc: Assoc(T;op),
mset_mon: mset_mon{s},
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
grp_id: e,
guard: {T}
Lemmas referenced :
mset_mon_wf,
mset_wf,
dset_wf,
abmonoid_properties,
mon_wf,
comm_wf,
grp_car_wf,
grp_op_wf,
mon_properties,
grp_sig_wf,
monoid_p_wf,
grp_id_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
equalityTransitivity,
equalitySymmetry,
isectElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
cumulativity,
productElimination,
sqequalRule
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. ((a + 0\{s\}) = a)
Date html generated:
2016_05_16-AM-07_47_07
Last ObjectModification:
2015_12_28-PM-06_03_42
Theory : mset
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