Nuprl Lemma : int-decr-map-find-prop
∀[Value:Type]
∀k:ℤ. ∀m:int-decr-map-type(Value).
((↑isl(int-decr-map-find(k;m))) ⇒ ((¬↑null(m)) ∧ (<k, outl(int-decr-map-find(k;m))> ∈ m)))
Proof
Definitions occuring in Statement :
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
l_member: (x ∈ l),
null: null(as),
outl: outl(x),
assert: ↑b,
isl: isl(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
universe: Type
Lemmas :
int-decr-map-find_wf,
not_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
l_member_wf,
squash_wf,
l_all_wf2,
equal-wf-base-T,
int_subtype_base,
assert_elim,
not_assert_elim,
btrue_neq_bfalse,
int-decr-map-type-member-sq-stable,
true_wf,
false_wf,
equal_wf,
int-decr-map-type_wf
\mforall{}[Value:Type]
\mforall{}k:\mBbbZ{}. \mforall{}m:int-decr-map-type(Value).
((\muparrow{}isl(int-decr-map-find(k;m))) {}\mRightarrow{} ((\mneg{}\muparrow{}null(m)) \mwedge{} (<k, outl(int-decr-map-find(k;m))> \mmember{} m)))
Date html generated:
2015_07_17-AM-08_22_52
Last ObjectModification:
2015_04_02-PM-05_43_58
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