Nuprl Lemma : union-nat-missing-prop
∀s1,s2:nat-missing-type(). ∀x:ℕ.
(↑member-nat-missing(x;union-nat-missing(s1;s2)) ⇐⇒ (↑member-nat-missing(x;s1)) ∨ (↑member-nat-missing(x;s2)))
Proof
Definitions occuring in Statement :
union-nat-missing: union-nat-missing(s1;s2),
member-nat-missing: member-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
nat: ℕ,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
union-nat-missing: union-nat-missing(s1;s2),
nat-missing-type: nat-missing-type(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
pi1: fst(t),
pi2: snd(t),
nat: ℕ,
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
top: Top,
member-nat-missing: member-nat-missing(i;s),
cand: A c∧ B,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}s1,s2:nat-missing-type(). \mforall{}x:\mBbbN{}.
(\muparrow{}member-nat-missing(x;union-nat-missing(s1;s2))
\mLeftarrow{}{}\mRightarrow{} (\muparrow{}member-nat-missing(x;s1)) \mvee{} (\muparrow{}member-nat-missing(x;s2)))
Date html generated:
2016_05_17-PM-01_45_38
Last ObjectModification:
2016_01_17-AM-11_37_51
Theory : datatype-signatures
Home
Index