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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ
Latex:
\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:
2016_05_17-PM-01_48_22
Last ObjectModification:
2015_12_28-PM-08_50_52
Theory : datatype-signatures
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