Nuprl Lemma : isEmpty-nat-missing-prop
∀s:nat-missing-type(). (↑isEmpty-nat-missing(s) 
⇐⇒ ∀x:ℕ. (¬↑member-nat-missing(x;s)))
Proof
Definitions occuring in Statement : 
isEmpty-nat-missing: isEmpty-nat-missing(s)
, 
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
, 
not: ¬A
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
isEmpty-nat-missing: isEmpty-nat-missing(s)
, 
nat-missing-type: nat-missing-type()
, 
pi2: snd(t)
, 
pi1: fst(t)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
top: Top
, 
uiff: uiff(P;Q)
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
nat: ℕ
, 
ge: i ≥ j 
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
member-nat-missing: member-nat-missing(i;s)
, 
sq_stable: SqStable(P)
, 
cand: A c∧ B
, 
squash: ↓T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
decidable: Dec(P)
, 
or: P ∨ Q
Latex:
\mforall{}s:nat-missing-type().  (\muparrow{}isEmpty-nat-missing(s)  \mLeftarrow{}{}\mRightarrow{}  \mforall{}x:\mBbbN{}.  (\mneg{}\muparrow{}member-nat-missing(x;s)))
Date html generated:
2016_05_17-PM-01_45_08
Last ObjectModification:
2016_01_17-AM-11_37_18
Theory : datatype-signatures
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