Nuprl Lemma : int-decr-map-fun
∀[Value:Type]. ∀[m:int-decr-map-type(Value)]. ∀[k:ℤ]. ∀[v1,v2:Value].
(v1 = v2 ∈ Value) supposing ((<k, v1> ∈ m) and (<k, v2> ∈ m))
Proof
Definitions occuring in Statement :
int-decr-map-type: int-decr-map-type(Value),
l_member: (x ∈ l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l_member: (x ∈ l),
int-decr-map-type: int-decr-map-type(Value),
exists: ∃x:A. B[x],
cand: A c∧ B,
all: ∀x:A. B[x],
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
pi2: snd(t),
squash: ↓T,
and: P ∧ Q,
prop: ℙ,
gt: i > j,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
pi1: fst(t),
so_apply: x[s1;s2],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
subtype_rel: A ⊆r B
Latex:
\mforall{}[Value:Type]. \mforall{}[m:int-decr-map-type(Value)]. \mforall{}[k:\mBbbZ{}]. \mforall{}[v1,v2:Value].
(v1 = v2) supposing ((<k, v1> \mmember{} m) and (<k, v2> \mmember{} m))
Date html generated:
2016_05_17-PM-01_47_50
Last ObjectModification:
2016_01_17-AM-11_37_01
Theory : datatype-signatures
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