Nuprl Lemma : int-decr-map-find_wf
∀[Value:Type]. ∀[k:ℤ]. ∀[m:int-decr-map-type(Value)].
(int-decr-map-find(k;m) ∈ {v:Value| (¬↑null(m)) ∧ (<k, v> ∈ m)} + (↓(∀p∈m.¬(k = (fst(p)) ∈ ℤ))))
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_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
null: null(as),
assert: ↑b,
uall: ∀[x:A]. B[x],
pi1: fst(t),
not: ¬A,
squash: ↓T,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
pair: <a, b>,
product: x:A × B[x],
union: left + right,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
pi1: fst(t),
so_apply: x[s1;s2],
gt: i > j,
subtype_rel: A ⊆r B,
or: P ∨ Q,
find-combine: find-combine(cmp;l),
list_ind: list_ind,
nil: [],
it: ⋅,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
iff: P ⇐⇒ Q,
cons: [a / b],
colength: colength(L),
guard: {T},
decidable: Dec(P),
sq_type: SQType(T),
less_than: a < b,
less_than': less_than'(a;b),
bfalse: ff,
has-value: (a)↓,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
uiff: uiff(P;Q),
bnot: ¬bb,
pi2: snd(t),
cand: A c∧ B,
rev_implies: P ⇐ Q,
nequal: a ≠ b ∈ T
Latex:
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[m:int-decr-map-type(Value)].
(int-decr-map-find(k;m) \mmember{} \{v:Value| (\mneg{}\muparrow{}null(m)) \mwedge{} (<k, v> \mmember{} m)\} + (\mdownarrow{}(\mforall{}p\mmember{}m.\mneg{}(k = (fst(p))))))
Date html generated:
2016_05_17-PM-01_48_01
Last ObjectModification:
2016_01_17-AM-11_38_03
Theory : datatype-signatures
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