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Signature symbols in this unit

Symbol	Specification	Kind	Type
# .	list-data	f	list('a) → nat
# .	stream-old	f	stream('a) → natinf
. '	list	f	'a → list('a)
. + .	nat-basic	f	nat × nat → nat
. + .	list-data	f	'a × list('a) → list('a)
. + .	list	f	list('a) × list('a) → list('a)
. + .	list	f	list('a) × 'a → list('a)
. + .	nat-inf	f	natinf × natinf → natinf
. + .	stream-old	f	'a × stream('a) → stream('a)
. + .	stream-old	f	stream('a) × stream('a) → stream('a)
. ++ .	list-dup	f	list('a) × 'a → list('a)
. +1	nat-basic	f	nat → nat
. +2 .	list	f	'a × 'a → list('a)
. - .	nat	pf	nat × nat → nat with λ n, m. n ≥ m
. -1	nat-basic	pf	nat → nat with λ n. n ≠ 0
. -1l .	list-del	f	list('a) × 'a → list('a)
. -l .	list-del	f	list('a) × 'a → list('a)
. -p .	list-del	f	list('a) × nat → list('a)
. .butlast	list-last	pf	list('a) → list('a) with λ x. x ≠ []
. .f	stream-basic	pf	stream('a) → nat → 'a with λ σ. λ m. ∃ nf. σ = ⌜nf⌝
. .foldLeft ( . )	list	f	list('a) × 'b × ('b × 'a → 'b) → 'b
. .head	list-data	pf	list('a) → 'a with λ x. x ≠ []
. .l	stream-basic	pf	stream('a) → list('a) with λ σ. finp(σ)
. .last	list-last	pf	list('a) → 'a with λ x. x ≠ []
. .n	nat-inf	pf	natinf → nat with λ n∞. n∞ ≠ ∞
. .tail	list-data	pf	list('a) → list('a) with λ x. x ≠ []
. < .	nat-basic	p	nat × nat
. < .	list-data	p	list('a) × list('a)
. < .	nat-inf	p	natinf × natinf
. > .	nat	p	nat × nat
. [ . := . ]	list-getput	pf	list('a) × nat × 'a → list('a) with λ x, n, a. n < # x
. [ . := . ]	stream-old	pf	stream('a) × nat × 'a → stream('a) with λ σ, n, a. finp(σ) → ⌜n⌝ < # σ
. [ . ]	list-getput	pf	list('a) × nat → 'a with λ x, n. n < # x
. [ . ]	stream-old	pf	stream('a) × nat → 'a with λ σ, n. finp(σ) → ⌜n⌝ < # σ
. ∈ .	list	p	'a × list('a)
. ≤ .	nat	p	nat × nat
. ≥ .	nat	p	nat × nat
. ⊑ .	list-last	p	list('a) × list('a)
. ⊑ .	stream-old	p	stream('a) × stream('a)
. ⊒ .	list-last	p	list('a) × list('a)
. from .	stream-old	f	(nat → 'a) × nat → nat → 'a
. from .	stream-old	pf	stream('a) × nat → stream('a) with λ σ, n. finp(σ) → ⌜n⌝ < # σ ∨ ⌜n⌝ = # σ
. from .	stream-old	pf	list('a) × nat → list('a) with λ x, n. n ≤ # x
. map .	list	f	list('a) × ('a → 'b) → list('b)
. to .	stream-old	f	(nat → 'a) × nat → list('a)
. to .	stream-old	pf	stream('a) × nat → stream('a) with λ σ, n. finp(σ) → ⌜n⌝ < # σ ∨ ⌜n⌝ = # σ
. to .	stream-old	pf	list('a) × nat → list('a) with λ x, n. n ≤ # x
. to∞ .	stream-old	pf	stream('a) × natinf → stream('a) with λ σ, n∞. finp(σ) → n∞ < # σ ∨ n∞ = # σ
[]	list-data	c	list('a)
[]	stream-old	c	stream('a)
σ	stream-old	v	stream('a)
∞	nat-inf	c	natinf
⌜ . ⌝	stream-basic	f	list('a) → stream('a)
⌜ . ⌝	stream-basic	f	(nat → 'a) → stream('a)
⌜ . ⌝	nat-inf	f	nat → natinf
a	stream-old	v	'a
butlastn	list-last	pf	nat × list('a) → list('a) with λ n, x. n ≤ # x
disj	list-dup	p	list('a) × list('a)
dups	list-dup	p	list('a)
fillfirst	list-last	f	nat × 'a × list('a) → list('a)
finp	stream-basic	p	stream('a)
firstn	list-del	pf	nat × list('a) → list('a) with λ n, x. n ≤ # x
frome	list-del	f	list('a) × 'a → list('a)
hd	stream-old	pf	stream('a) → 'a with λ σ. σ ≠ []
lastn	list-del	pf	nat × list('a) → list('a) with λ n, x. n ≤ # x
list	list-data	s
m	stream-old	v	nat
min	nat-inf	f	natinf × natinf → natinf
mklist	list-last	f	'a × nat → list('a)
n	stream-old	v	nat
n∞	stream-old	v	natinf
nat	nat-basic	s
natinf	nat-inf	s
nf	stream-old	v	nat → 'a
pos	list-del	f	'a × list('a) → nat
restn	list-del	pf	nat × list('a) → list('a) with λ n, x. n ≤ # x
rev	list-last	f	list('a) → list('a)
rmdup	list-dup	f	list('a) → list('a)
stream	stream-basic	s
sublist	list-del	pf	nat × nat × list('a) → list('a) with λ n, m, x. n + m ≤ # x
tl	stream-old	pf	stream('a) → stream('a) with λ σ. σ ≠ []
x	stream-old	v	list('a)
y	stream-old	v	list('a)
z	stream-old	v	list('a)