Nuprl Lemma : oal_mon_wf
∀a:LOSet. ∀b:AbDMon. (oal_mon(a;b) ∈ AbDMon)
Proof
Definitions occuring in Statement :
oal_mon: oal_mon(a;b),
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
oal_mon: oal_mon(a;b),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
uimplies: b supposing a,
assoc: Assoc(T;op),
infix_ap: x f y,
ident: Ident(T;op;id),
and: P ∧ Q,
comm: Comm(T;op)
Lemmas referenced :
mk_abdmonoid,
set_car_wf,
oalist_wf,
dset_wf,
set_eq_wf,
btrue_wf,
oal_merge_wf2,
oal_nil_wf,
abdmonoid_wf,
loset_wf,
dset_properties,
oal_merge_assoc,
oal_nil_ident_r,
oal_nil_ident_l,
oal_merge_comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
isect_memberFormation,
introduction,
isect_memberEquality,
axiomEquality,
independent_pairFormation,
productElimination,
independent_pairEquality
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. (oal\_mon(a;b) \mmember{} AbDMon)
Date html generated:
2016_05_16-AM-08_18_34
Last ObjectModification:
2015_12_28-PM-06_26_44
Theory : polynom_2
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