Nuprl Lemma : int-decr-map-inDom-cons
∀[Value:Type]. ∀[k:ℤ]. ∀[u:ℤ × Value]. ∀[v:int-decr-map-type(Value)].
(k ≤ (fst(u))) supposing ((↑int-decr-map-inDom(k;[u / v])) and (∀y:ℤ × Value. ((y ∈ v) ⇒ ((fst(u)) > (fst(y))))))
Proof
Definitions occuring in Statement :
int-decr-map-inDom: int-decr-map-inDom(k;m),
int-decr-map-type: int-decr-map-type(Value),
l_member: (x ∈ l),
cons: [a / b],
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
gt: i > j,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
int: ℤ,
universe: Type
Lemmas :
l-ordered-cons,
l-ordered_wf,
gt_wf,
int-decr-map-inDom-prop1,
int-decr-map-inDom-prop,
int-decr-map-find_wf,
not_wf,
assert_wf,
null_wf3,
subtype_rel_set,
list_wf,
top_wf,
subtype_rel_list,
l_member_wf,
squash_wf,
l_all_wf2,
equal-wf-base-T,
int_subtype_base,
cons_member,
le_weakening,
and_wf,
equal_wf,
pi1_wf_top,
subtype_rel_product,
le_wf,
le_weakening2,
true_wf,
false_wf,
less_than_wf,
int-decr-map-inDom_wf,
cons_wf,
all_wf,
int-decr-map-type_wf
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[u:\mBbbZ{} \mtimes{} Value]. \mforall{}[v:int-decr-map-type(Value)].
(k \mleq{} (fst(u))) supposing
((\muparrow{}int-decr-map-inDom(k;[u / v])) and
(\mforall{}y:\mBbbZ{} \mtimes{} Value. ((y \mmember{} v) {}\mRightarrow{} ((fst(u)) > (fst(y))))))
Date html generated:
2015_07_17-AM-08_23_05
Last ObjectModification:
2015_04_02-PM-05_44_10
Home
Index