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
Home
Index