Nuprl Lemma : int-decr-map-inDom-cons
∀[Value:Type]. ∀[k:ℤ]. ∀[u:ℤ × Value]. ∀[v:int-decr-map-type(Value)].
(k ≤ (fst(u))) supposing ((↑int-decr-map-inDom(k;[u / v])) and (∀y:ℤ × Value. ((y ∈ v) ⇒ ((fst(u)) > (fst(y))))))
Proof
Definitions occuring in Statement :
int-decr-map-inDom: int-decr-map-inDom(k;m),
int-decr-map-type: int-decr-map-type(Value),
l_member: (x ∈ l),
cons: [a / b],
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
gt: i > j,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
int-decr-map-type: int-decr-map-type(Value),
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
gt: i > j,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
so_lambda: λ2x.t[x],
pi1: fst(t),
so_apply: x[s],
top: Top,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
or: P ∨ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
bfalse: ff,
le: A ≤ B
Latex:
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[u:\mBbbZ{} \mtimes{} Value]. \mforall{}[v:int-decr-map-type(Value)].
(k \mleq{} (fst(u))) supposing
((\muparrow{}int-decr-map-inDom(k;[u / v])) and
(\mforall{}y:\mBbbZ{} \mtimes{} Value. ((y \mmember{} v) {}\mRightarrow{} ((fst(u)) > (fst(y))))))
Date html generated:
2016_05_17-PM-01_48_28
Last ObjectModification:
2016_01_17-AM-11_37_11
Theory : datatype-signatures
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