Nuprl Lemma : assert-in-missing-nat-iff
∀i:ℕ. ∀missing:{l:ℕ List| l-ordered(ℕ;x,y.x < y;l)} . (↑in-missing(i;missing) ⇐⇒ (i ∈ missing))
Proof
Definitions occuring in Statement :
in-missing: in-missing(i;missing),
l_member: (x ∈ l),
list: T List,
nat: ℕ,
assert: ↑b,
less_than: a < b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]}
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],
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
rev_implies: P ⇐ Q,
sq_stable: SqStable(P),
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_apply: x[s],
false: False,
in-missing: in-missing(i;missing),
top: Top,
uiff: uiff(P;Q),
or: P ∨ Q,
cand: A c∧ B,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T
Latex:
\mforall{}i:\mBbbN{}. \mforall{}missing:\{l:\mBbbN{} List| l-ordered(\mBbbN{};x,y.x < y;l)\} . (\muparrow{}in-missing(i;missing) \mLeftarrow{}{}\mRightarrow{} (i \mmember{} missing))
Date html generated:
2016_05_17-PM-01_44_48
Last ObjectModification:
2016_01_17-AM-11_37_16
Theory : datatype-signatures
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