Nuprl Lemma : oal_umap_wf
∀s:LOSet. ∀g:AbDMon. ∀h:AbMon. ∀f:|s| ⟶ |g| ⟶ |h|. (umap(h,f) ∈ |oal(s;g)| ⟶ |h|)
Proof
Definitions occuring in Statement :
oal_umap: umap(h,f),
oalist: oal(a;b),
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
abdmonoid: AbDMon,
abmonoid: AbMon,
grp_car: |g|,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
oal_umap: umap(h,f),
all: ∀x:A. B[x],
member: t ∈ T,
tlambda: λx:T. b[x],
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
dset: DSet,
uall: ∀[x:A]. B[x],
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
dset_list: s List,
set_prod: s × t,
dset_of_mon: g↓set,
so_apply: x[s],
abmonoid: AbMon
Lemmas referenced :
mset_for_wf,
abmonoid_subtype_iabmonoid,
lookup_wf,
grp_car_wf,
grp_id_wf,
set_car_wf,
oalist_wf,
dset_wf,
oal_dom_wf,
abdmonoid_abmonoid,
abmonoid_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
isectElimination,
because_Cache,
functionEquality
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDMon. \mforall{}h:AbMon. \mforall{}f:|s| {}\mrightarrow{} |g| {}\mrightarrow{} |h|. (umap(h,f) \mmember{} |oal(s;g)| {}\mrightarrow{} |h|)
Date html generated:
2016_05_16-AM-08_22_57
Last ObjectModification:
2015_12_28-PM-06_24_55
Theory : polynom_2
Home
Index