Nuprl Lemma : mset_mem_wf
∀s:DSet. ∀x:|s|. ∀a:MSet{s}. (x ∈b a ∈ 𝔹)
Proof
Definitions occuring in Statement :
mset_mem: mset_mem,
mset: MSet{s},
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
mset_mem: mset_mem,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
mset: MSet{s},
quotient: x,y:A//B[x; y],
and: P ∧ Q,
prop: ℙ,
squash: ↓T,
implies: P ⇒ Q,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mset_wf,
set_car_wf,
dset_wf,
bool_wf,
equal-wf-base,
list_wf,
permr_wf,
equal_wf,
squash_wf,
true_wf,
mem_functionality_wrt_permr,
mem_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
setElimination,
rename,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
productEquality,
because_Cache,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}x:|s|. \mforall{}a:MSet\{s\}. (x \mmember{}\msubb{} a \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-09_59_08
Last ObjectModification:
2017_03_03-PM-01_00_01
Theory : mset
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