Nuprl Lemma : mset_map_id
∀s:DSet. ∀a:MSet{s}. (msmap{s,s}(Id{|s|};a) = a ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_map: msmap{s,s'}(f;a),
mset: MSet{s},
tidentity: Id{T},
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,
uall: ∀[x:A]. B[x],
dset: DSet,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
tidentity: Id{T},
mset_map: msmap{s,s'}(f;a),
squash: ↓T,
subtype_rel: A ⊆r B,
true: True,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
equal_mset_elim,
map_wf,
set_car_wf,
tidentity_wf,
iff_transitivity,
all_wf,
dset_wf,
mset_wf,
equal_wf,
mset_map_wf,
list_wf,
mk_mset_wf,
all_mset_elim,
sq_stable__equal,
squash_wf,
true_wf,
subtype_rel_poset,
eqfun_p_wf,
set_eq_wf,
mset_map_char,
iff_weakening_equal,
permr_wf,
permr_weakening,
map_id
Rules used in proof :
cut,
addLevel,
allFunctionality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
setElimination,
rename,
hypothesis,
because_Cache,
productElimination,
independent_functionElimination,
instantiate,
sqequalRule,
lambdaEquality,
cumulativity,
independent_pairFormation,
lambdaFormation,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
dependent_set_memberEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
levelHypothesis,
allLevelFunctionality
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. (msmap\{s,s\}(Id\{|s|\};a) = a)
Date html generated:
2017_10_01-AM-09_59_45
Last ObjectModification:
2017_03_03-PM-01_01_08
Theory : mset
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