Nuprl Lemma : equal_mset_elim
∀s:DSet. ∀as,bs:|s| List. (mk_mset(as) = mk_mset(bs) ∈ MSet{s} ⇐⇒ as ≡(|s|) bs)
Proof
Definitions occuring in Statement :
mk_mset: mk_mset(as),
mset: MSet{s},
permr: as ≡(T) bs,
list: T List,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
prop: ℙ,
mk_mset: mk_mset(as),
eq_mset: eq_mset{s}(a,b),
subtype_rel: A ⊆r B,
mset: MSet{s},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
list_wf,
set_car_wf,
dset_wf,
assert_of_bpermr,
permr_wf,
iff_wf,
equal_wf,
mset_wf,
mk_mset_wf,
assert_wf,
bpermr_wf,
assert_of_eq_mset,
subtype_quotient,
permr_equiv_rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
addLevel,
productElimination,
independent_pairFormation,
impliesFunctionality,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
sqequalRule,
lambdaEquality,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. (mk\_mset(as) = mk\_mset(bs) \mLeftarrow{}{}\mRightarrow{} as \mequiv{}(|s|) bs)
Date html generated:
2016_05_16-AM-07_47_01
Last ObjectModification:
2015_12_28-PM-06_03_52
Theory : mset
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