Nuprl Lemma : int-decr-map-find-prop2
∀[Value:Type]. ∀[k:ℤ]. ∀[m:int-decr-map-type(Value)].
(∀p∈m.¬(k = (fst(p)) ∈ ℤ)) supposing ¬↑isl(int-decr-map-find(k;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_all: (∀x∈L.P[x]),
assert: ↑b,
isl: isl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
not: ¬A,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[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,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
uimplies: b supposing a,
not: ¬A,
true: True,
false: False,
l_all: (∀x∈L.P[x]),
bfalse: ff,
squash: ↓T,
top: Top,
sq_stable: SqStable(P),
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
less_than: a < b
Latex:
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[m:int-decr-map-type(Value)].
(\mforall{}p\mmember{}m.\mneg{}(k = (fst(p)))) supposing \mneg{}\muparrow{}isl(int-decr-map-find(k;m))
Date html generated:
2016_05_17-PM-01_48_09
Last ObjectModification:
2016_01_17-AM-11_36_59
Theory : datatype-signatures
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