Nuprl Lemma : map-sig-inDom-prop
∀[Key,Value:Type]. ∀[ms:map-sig{i:l}(Key;Value)]. ∀[k:Key]. ∀[m:map-sig-map(ms)].
(↑(map-sig-inDom(ms) k m) ⇐⇒ ↑isl(map-sig-find(ms) k m))
Proof
Definitions occuring in Statement :
map-sig-inDom: map-sig-inDom(m),
map-sig-find: map-sig-find(m),
map-sig-map: map-sig-map(m),
map-sig: map-sig{i:l}(Key;Value),
assert: ↑b,
isl: isl(x),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
apply: f a,
universe: Type
Lemmas :
subtype_rel_self,
valueall-type_wf,
deq_wf,
unit_wf2,
bool_wf,
all_wf,
iff_wf,
assert_wf,
isl_wf,
not_wf,
equal_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bnot_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
assert_of_bnot,
it_wf,
set_wf,
sq_stable__iff,
map-sig-inDom_wf,
map-sig-find_wf,
sq_stable__assert,
map-sig-map_wf,
map-sig_wf
\mforall{}[Key,Value:Type]. \mforall{}[ms:map-sig\{i:l\}(Key;Value)]. \mforall{}[k:Key]. \mforall{}[m:map-sig-map(ms)].
(\muparrow{}(map-sig-inDom(ms) k m) \mLeftarrow{}{}\mRightarrow{} \muparrow{}isl(map-sig-find(ms) k m))
Date html generated:
2015_07_17-AM-08_22_15
Last ObjectModification:
2015_04_02-PM-05_43_41
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