Nuprl Lemma : count_lmin
∀s:DSet. ∀as,bs:|s| List. ∀c:|s|. ((c #∈ lmin(s;as;bs)) = imin(c #∈ as;c #∈ bs) ∈ ℤ)
Proof
Definitions occuring in Statement :
lmin: lmin(s;as;bs),
count: a #∈ as,
imin: imin(a;b),
list: T List,
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],
lmin: lmin(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,
nat: ℕ
Lemmas referenced :
set_car_wf,
list_wf,
dset_wf,
diff_wf,
imin_wf,
count_wf,
equal_wf,
squash_wf,
true_wf,
count_diff,
ndiff_wf,
iff_weakening_equal,
count_bounds,
le_wf,
ndiff_ndiff_eq_imin
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
intEquality,
dependent_functionElimination,
because_Cache,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_set_memberEquality
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. \mforall{}c:|s|. ((c \#\mmember{} lmin(s;as;bs)) = imin(c \#\mmember{} as;c \#\mmember{} bs))
Date html generated:
2017_10_01-AM-09_56_48
Last ObjectModification:
2017_03_03-PM-00_58_12
Theory : list_2
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