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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
int-decr-map-type: int-decr-map-type(Value),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cand: A c∧ B,
not: ¬A,
false: False,
sq_stable: SqStable(P),
squash: ↓T,
bfalse: ff
Latex:
\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:
2016_05_17-PM-01_48_07
Last ObjectModification:
2016_01_17-AM-11_36_54
Theory : datatype-signatures
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