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Signature symbols in this unit

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