Nuprl Lemma : remove-nat-missing-prop
∀s:nat-missing-type(). ∀x,y:ℕ.
(↑member-nat-missing(x;remove-nat-missing(y;s)) ⇐⇒ (¬(x = y ∈ ℕ)) ∧ (↑member-nat-missing(x;s)))
Proof
Definitions occuring in Statement :
remove-nat-missing: remove-nat-missing(i;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,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
remove-nat-missing: remove-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
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,
pi1: fst(t),
pi2: snd(t),
iff: P ⇐⇒ Q,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
sq_stable: SqStable(P),
squash: ↓T,
decidable: Dec(P),
true: True,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
has-value: (a)↓,
le: A ≤ B,
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
nequal: a ≠ b ∈ T ,
lelt: i ≤ j < k,
less_than: a < b,
last: last(L),
int-minus-comparison-inc: int-minus-comparison-inc(f),
comparison: comparison(T),
rev_uimplies: rev_uimplies(P;Q),
trans: Trans(T;x,y.E[x; y]),
l-ordered: l-ordered(T;x,y.R[x; y];L),
le_int: i ≤z j,
less_than': less_than'(a;b),
cons: [a / b],
iseg: l1 ≤ l2,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
st_anti_sym: StAntiSym(T;x,y.R[x; y]),
irrefl: Irrefl(T;x,y.E[x; y])
Latex:
\mforall{}s:nat-missing-type(). \mforall{}x,y:\mBbbN{}.
(\muparrow{}member-nat-missing(x;remove-nat-missing(y;s)) \mLeftarrow{}{}\mRightarrow{} (\mneg{}(x = y)) \mwedge{} (\muparrow{}member-nat-missing(x;s)))
Date html generated:
2016_05_17-PM-01_46_27
Last ObjectModification:
2016_01_17-AM-11_38_24
Theory : datatype-signatures
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