Nuprl Lemma : mset_mem_mon_for_union
∀s,s':DSet. ∀a:MSet{s}. ∀e:|s| ⟶ MSet{s'}. ∀x:|s'|. x ∈b msFor{<MSet{s'},⋃,0>} y ∈ a. e[y] = ∃b{s} y ∈ a. (x ∈b e[y])
Proof
Definitions occuring in Statement :
mset_union_mon: <MSet{s},⋃,0>,
mset_for: mset_for,
mset_mem: mset_mem,
mset: MSet{s},
bool: 𝔹,
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T,
bor_mon: <𝔹,∨b>,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
subtype_rel: A ⊆r B,
monoid_hom: MonHom(M1,M2),
mset_union_mon: <MSet{s},⋃,0>,
grp_car: |g|,
pi1: fst(t),
bor_mon: <𝔹,∨b>,
abmonoid: AbMon,
mon: Mon,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
set_car_wf,
mset_wf,
dset_wf,
dist_hom_over_mset_for,
mset_union_mon_wf,
abmonoid_subtype_iabmonoid,
bor_mon_wf,
mset_union_bor_mon_hom,
mset_mem_wf,
bool_wf,
grp_car_wf,
abmonoid_wf,
monoid_hom_p_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
functionEquality,
dependent_functionElimination,
sqequalRule,
applyEquality,
dependent_set_memberEquality,
lambdaEquality,
because_Cache
Latex:
\mforall{}s,s':DSet. \mforall{}a:MSet\{s\}. \mforall{}e:|s| {}\mrightarrow{} MSet\{s'\}. \mforall{}x:|s'|.
x \mmember{}\msubb{} msFor\{<MSet\{s'\},\mcup{},0>\} y \mmember{} a. e[y] = \mexists{}\msubb{}\{s\} y \mmember{} a. (x \mmember{}\msubb{} e[y])
Date html generated:
2016_05_16-AM-07_49_57
Last ObjectModification:
2015_12_28-PM-06_01_25
Theory : mset
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