Nuprl Lemma : int-decr-map-inDom-prop1
∀[Value:Type]
∀k:ℤ. ∀m:int-decr-map-type(Value).
(¬↑null(m)) ∧ (<k, outl(int-decr-map-find(k;m))> ∈ m) supposing ↑int-decr-map-inDom(k;m)
Proof
Definitions occuring in Statement :
int-decr-map-inDom: int-decr-map-inDom(k;m)
,
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
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
all: ∀x:A. B[x]
,
not: ¬A
,
and: P ∧ Q
,
pair: <a, b>
,
product: x:A × B[x]
,
int: ℤ
,
universe: Type
Lemmas :
assert_witness,
int-decr-map-inDom_wf,
int-decr-map-inDom-prop,
int-decr-map-find-prop,
assert_wf,
int-decr-map-type_wf
\mforall{}[Value:Type]
\mforall{}k:\mBbbZ{}. \mforall{}m:int-decr-map-type(Value).
(\mneg{}\muparrow{}null(m)) \mwedge{} (<k, outl(int-decr-map-find(k;m))> \mmember{} m) supposing \muparrow{}int-decr-map-inDom(k;m)
Date html generated:
2015_07_17-AM-08_23_01
Last ObjectModification:
2015_04_02-PM-05_44_06
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