Nuprl Lemma : mset_mem_functionality_wrt_bsubmset
∀s:DSet. ∀a:FiniteSet{s}. ∀b:MSet{s}. ∀u:|s|. ((↑(a ⊆b b)) ⇒ (↑(u ∈b a ⇒b (u ∈b b))))
Proof
Definitions occuring in Statement :
bsubmset: a ⊆b b,
mset_mem: mset_mem,
finite_set: FiniteSet{s},
mset: MSet{s},
bimplies: p ⇒b q,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
finite_set: FiniteSet{s},
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
dset: DSet
Lemmas referenced :
iff_weakening_uiff,
assert_wf,
bimplies_wf,
mset_mem_wf,
isect_wf,
assert_of_bimplies,
bsubmset_wf,
set_car_wf,
mset_wf,
finite_set_wf,
dset_wf,
mem_bsubmset,
assert_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
isect_memberEquality,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
lambdaEquality,
independent_functionElimination,
productElimination,
isect_memberFormation,
introduction
Latex:
\mforall{}s:DSet. \mforall{}a:FiniteSet\{s\}. \mforall{}b:MSet\{s\}. \mforall{}u:|s|. ((\muparrow{}(a \msubseteq{}\msubb{} b)) {}\mRightarrow{} (\muparrow{}(u \mmember{}\msubb{} a {}\mRightarrow{}\msubb{} (u \mmember{}\msubb{} b))))
Date html generated:
2016_05_16-AM-07_51_04
Last ObjectModification:
2015_12_28-PM-06_02_39
Theory : mset
Home
Index