Nuprl Lemma : int-decr-map-type-member-sq-stable
∀[Value:Type]. ∀k:ℤ. ∀v:Value. ∀m:int-decr-map-type(Value). SqStable((<k, v> ∈ m))
Proof
Definitions occuring in Statement :
int-decr-map-type: int-decr-map-type(Value),
l_member: (x ∈ l),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
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],
sq_stable: SqStable(P),
implies: P ⇒ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
member: t ∈ T,
squash: ↓T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
top: Top,
int-decr-map-type: int-decr-map-type(Value),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
l_exists: (∃x∈L. P[x]),
cand: A c∧ B,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
prop: ℙ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
pi1: fst(t),
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
less_than: a < b,
true: True
Latex:
\mforall{}[Value:Type]. \mforall{}k:\mBbbZ{}. \mforall{}v:Value. \mforall{}m:int-decr-map-type(Value). SqStable((<k, v> \mmember{} m))
Date html generated:
2016_05_17-PM-01_47_54
Last ObjectModification:
2016_01_17-AM-11_37_29
Theory : datatype-signatures
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