Nuprl Lemma : int-decr-map-inDom-prop
∀[Value:Type]. ∀[k:ℤ]. ∀[m:int-decr-map-type(Value)]. (↑int-decr-map-inDom(k;m) ⇐⇒ ↑isl(int-decr-map-find(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),
assert: ↑b,
isl: isl(x),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
int: ℤ,
universe: Type
Definitions unfolded in proof :
int-decr-map-inDom: int-decr-map-inDom(k;m),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
int-decr-map-type: int-decr-map-type(Value),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
uimplies: b supposing a,
top: Top
Latex:
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[m:int-decr-map-type(Value)].
(\muparrow{}int-decr-map-inDom(k;m) \mLeftarrow{}{}\mRightarrow{} \muparrow{}isl(int-decr-map-find(k;m)))
Date html generated:
2016_05_17-PM-01_48_20
Last ObjectModification:
2015_12_28-PM-08_50_56
Theory : datatype-signatures
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