Nuprl Lemma : eq_mset_wf
∀s:DSet. ∀a,b:MSet{s}. (eq_mset{s}(a,b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
eq_mset: eq_mset{s}(a,b),
mset: MSet{s},
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
eq_mset: eq_mset{s}(a,b),
mset: MSet{s},
quotient: x,y:A//B[x; y],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
dset: DSet,
prop: ℙ,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mset_wf,
dset_wf,
bool_wf,
equal-wf-base,
list_wf,
set_car_wf,
permr_wf,
iff_imp_equal_bool,
bpermr_wf,
assert_of_bpermr,
assert_wf,
iff_wf,
permr_functionality_wrt_permr
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
pointwiseFunctionalityForEquality,
sqequalRule,
pertypeElimination,
productElimination,
productEquality,
isectElimination,
setElimination,
rename,
because_Cache,
independent_isectElimination,
addLevel,
independent_pairFormation,
impliesFunctionality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. (eq\_mset\{s\}(a,b) \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-07_46_54
Last ObjectModification:
2015_12_28-PM-06_03_34
Theory : mset
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