Nuprl Lemma : fset_of_mset_mem
∀s:DSet. ∀a:MSet{s}. ∀c:|s|. c ∈b fset_of_mset(s;a) = c ∈b a
Proof
Definitions occuring in Statement :
fset_of_mset: fset_of_mset(s;a),
mset_mem: mset_mem,
mset: MSet{s},
bool: 𝔹,
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
guard: {T},
dset: DSet,
fset_of_mset: fset_of_mset(s;a),
top: Top,
mset_union_mon: <MSet{s},⋃,0>,
grp_id: e,
pi2: snd(t),
pi1: fst(t),
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
grp_car: |g|,
abmonoid: AbMon,
mon: Mon,
true: True,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
infix_ap: x f y,
bor_mon: <𝔹,∨b>,
grp_op: *
Lemmas referenced :
mset_ind_a,
equal_wf,
bool_wf,
mset_mem_wf,
fset_of_mset_wf,
mset_wf,
set_car_wf,
dset_wf,
sq_stable__equal,
mset_for_null_lemma,
mset_mem_null_lemma,
bfalse_wf,
all_wf,
squash_wf,
true_wf,
mset_mem_char,
mset_for_wf,
mset_union_mon_wf,
abmonoid_subtype_iabmonoid,
mset_inj_wf,
grp_car_wf,
abmonoid_wf,
iff_weakening_equal,
mset_for_functionality,
bor_mon_wf,
set_eq_wf,
mset_for_mset_inj,
infix_ap_wf,
assert_wf,
mset_sum_wf,
grp_op_wf,
mset_for_mset_sum,
fset_mem_union,
bor_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
isectElimination,
hypothesis,
independent_functionElimination,
setElimination,
rename,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
equalityUniverse,
levelHypothesis
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. \mforall{}c:|s|. c \mmember{}\msubb{} fset\_of\_mset(s;a) = c \mmember{}\msubb{} a
Date html generated:
2017_10_01-AM-10_00_17
Last ObjectModification:
2017_03_03-PM-01_01_31
Theory : mset
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