Nuprl Lemma : assert-member-nat-missing
∀[i:ℕ]. ∀[s:nat-missing-type()]. (↑member-nat-missing(i;s) ⇐⇒ (i ≤ (fst(s))) ∧ (¬(i ∈ snd(s))))
Proof
Definitions occuring in Statement :
member-nat-missing: member-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
l_member: (x ∈ l),
nat: ℕ,
assert: ↑b,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
le: A ≤ B,
iff: P ⇐⇒ Q,
not: ¬A,
and: P ∧ Q
Definitions unfolded in proof :
member-nat-missing: member-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
pi1: fst(t),
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
pi2: snd(t),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_apply: x[s],
cand: A c∧ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
le: A ≤ B
Latex:
\mforall{}[i:\mBbbN{}]. \mforall{}[s:nat-missing-type()]. (\muparrow{}member-nat-missing(i;s) \mLeftarrow{}{}\mRightarrow{} (i \mleq{} (fst(s))) \mwedge{} (\mneg{}(i \mmember{} snd(s))))
Date html generated:
2016_05_17-PM-01_44_56
Last ObjectModification:
2015_12_28-PM-08_52_16
Theory : datatype-signatures
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