Nuprl Lemma : add-nat-missing-prop
∀s:nat-missing-type(). ∀x,y:ℕ.
(↑member-nat-missing(x;add-nat-missing(y;s)) ⇐⇒ (x = y ∈ ℕ) ∨ (↑member-nat-missing(x;s)))
Proof
Definitions occuring in Statement :
add-nat-missing: add-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,
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
add-nat-missing: add-nat-missing(i;s),
member-nat-missing: member-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
nat: ℕ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
bfalse: ff,
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
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,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
l-ordered: l-ordered(T;x,y.R[x; y];L),
nequal: a ≠ b ∈ T
Latex:
\mforall{}s:nat-missing-type(). \mforall{}x,y:\mBbbN{}.
(\muparrow{}member-nat-missing(x;add-nat-missing(y;s)) \mLeftarrow{}{}\mRightarrow{} (x = y) \mvee{} (\muparrow{}member-nat-missing(x;s)))
Date html generated:
2016_05_17-PM-01_45_24
Last ObjectModification:
2016_01_17-AM-11_38_09
Theory : datatype-signatures
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