Nuprl Lemma : bsubmset_wf
∀s:DSet. ∀a,b:MSet{s}. (a ⊆b b ∈ 𝔹)
Proof
Definitions occuring in Statement :
bsubmset: a ⊆b b,
mset: MSet{s},
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
bsubmset: a ⊆b b,
all: ∀x:A. B[x],
member: t ∈ T,
mset: MSet{s},
quotient: x,y:A//B[x; y],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
dset: DSet,
implies: P ⇒ Q,
prop: ℙ,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
bool_wf,
list_wf,
set_car_wf,
permr_wf,
equal_wf,
equal-wf-base,
mset_wf,
dset_wf,
bsublist_wf,
squash_wf,
true_wf,
bsublist_functionality_wrt_permr,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
introduction,
extract_by_obid,
hypothesis,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
equalitySymmetry,
isectElimination,
setElimination,
rename,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
productEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. (a \msubseteq{}\msubb{} b \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-10_00_19
Last ObjectModification:
2017_03_03-PM-01_01_28
Theory : mset
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