Nuprl Definition : correct-sort-arity
correct-sort-arity(sort;arity;t) ==
(¬↑isvarterm(t))
⇒ let bts = term-bts(t) in
let f = term-opr(t) in
(||bts|| = ||arity f|| ∈ ℤ)
∧ (∀i:ℕ||bts||. ((||fst(bts[i])|| = (fst(arity f[i])) ∈ ℤ) ∧ ((sort (snd(bts[i]))) = (snd(arity f[i])) ∈ ℤ)))
Definitions occuring in Statement :
term-bts: term-bts(t),
term-opr: term-opr(t),
isvarterm: isvarterm(t),
select: L[n],
length: ||as||,
int_seg: {i..j-},
assert: ↑b,
let: let,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions occuring in definition :
implies: P ⇒ Q,
not: ¬A,
assert: ↑b,
isvarterm: isvarterm(t),
term-bts: term-bts(t),
let: let,
term-opr: term-opr(t),
all: ∀x:A. B[x],
int_seg: {i..j-},
natural_number: $n,
and: P ∧ Q,
length: ||as||,
pi1: fst(t),
equal: s = t ∈ T,
int: ℤ,
pi2: snd(t),
select: L[n],
apply: f a
FDL editor aliases :
correct-sort-arity
Latex:
correct-sort-arity(sort;arity;t) ==
(\mneg{}\muparrow{}isvarterm(t))
{}\mRightarrow{} let bts = term-bts(t) in
let f = term-opr(t) in
(||bts|| = ||arity f||)
\mwedge{} (\mforall{}i:\mBbbN{}||bts||
((||fst(bts[i])|| = (fst(arity f[i]))) \mwedge{} ((sort (snd(bts[i]))) = (snd(arity f[i])))))
Date html generated:
2020_05_19-PM-09_58_08
Last ObjectModification:
2020_03_11-PM-03_52_14
Theory : terms
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