Nuprl Lemma : count_lmax
∀s:DSet. ∀as,bs:|s| List. ∀c:|s|. ((c #∈ lmax(s;as;bs)) = imax(c #∈ as;c #∈ bs) ∈ ℤ)
Proof
Definitions occuring in Statement :
lmax: lmax(s;as;bs),
count: a #∈ as,
list: T List,
imax: imax(a;b),
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
lmax: lmax(s;as;bs),
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
true: True,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
set_car_wf,
list_wf,
dset_wf,
diff_wf,
imax_wf,
count_wf,
ndiff_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
count_append,
subtype_rel_self,
add_functionality_wrt_eq,
count_diff,
iff_weakening_equal,
ndiff_add_eq_imax
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
inhabitedIsType,
intEquality,
dependent_functionElimination,
natural_numberEquality,
because_Cache,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. \mforall{}c:|s|. ((c \#\mmember{} lmax(s;as;bs)) = imax(c \#\mmember{} as;c \#\mmember{} bs))
Date html generated:
2019_10_16-PM-01_04_43
Last ObjectModification:
2018_10_08-AM-10_14_52
Theory : list_2
Home
Index