Nuprl Lemma : add-nat-missing_wf
∀[i:ℕ]. ∀[s:nat-missing-type()].  (add-nat-missing(i;s) ∈ nat-missing-type())
Proof
Definitions occuring in Statement : 
add-nat-missing: add-nat-missing(i;s)
, 
nat-missing-type: nat-missing-type()
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
add-nat-missing: add-nat-missing(i;s)
, 
nat-missing-type: nat-missing-type()
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
prop: ℙ
, 
guard: {T}
, 
sq_stable: SqStable(P)
, 
squash: ↓T
, 
ge: i ≥ j 
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
top: Top
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
bfalse: ff
, 
sq_type: SQType(T)
, 
bnot: ¬bb
, 
assert: ↑b
, 
cand: A c∧ B
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Latex:
\mforall{}[i:\mBbbN{}].  \mforall{}[s:nat-missing-type()].    (add-nat-missing(i;s)  \mmember{}  nat-missing-type())
Date html generated:
2016_05_17-PM-01_45_18
Last ObjectModification:
2016_01_17-AM-11_37_59
Theory : datatype-signatures
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