[Imprint][Data Privacy Statement][E-Mail]

Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Signature symbols in this unit

Symbol	Specification	Kind	Type
# .	natset	f	natset → nat
# .	matrixops	f	vector → nat
# .	sparsearray	f	sparsearray → nat
# .	sparsearray	f	npset → nat
#c .	matrix	f	matrix → nat
#r .	matrix	f	matrix → nat
. * .	ring	f	elem × elem → elem
. * .	matrixops	pf	matrix × matrix → matrix with λ mx1, mx2. #c mx1 = #r mx2
. * .	matrixops	pf	matrix × vector → vector with λ mx, vec. #r mx = # vec
. * .	matrixops	pf	vector × matrix → vector with λ vec, mx. #c mx = # vec
. * .	matrixops	pf	vector × vector → elem with λ vec1, vec2. # vec1 = # vec2
. + .	nat-basic	f	nat × nat → nat
. + .	ring	f	elem × elem → elem
. + .	matrixops	pf	matrix × matrix → matrix with λ mx1, mx2. #r mx1 = #r mx2 ∧ #r mxc = #c mx2
. + .	matrixops	pf	vector × vector → vector with λ vec1, vec2. # vec1 = # vec2
. ++ .	natset	f	natset × nat → natset
. ++ .	sparsearray	f	npset × natpair → npset
. +1	nat-basic	f	nat → nat
. - .	nat	pf	nat × nat → nat with λ n, m. n ≥ m
. -- .	natset	f	natset × nat → natset
. -- .	sparsearray	f	sparsearray × natpair → sparsearray
. -- .	sparsearray	f	npset × natpair → npset
. -1	nat-basic	pf	nat → nat with λ n. n ≠ 0
. .c	natpair	f	natpair → nat
. .r	natpair	f	natpair → nat
. .toMatrix ( . )	VerifyThis3-sequential	f	sparsearray × nat × nat → matrix
. < .	nat-basic	p	nat × nat
. > .	nat	p	nat × nat
. [ . ]	sparsearray	f	sparsearray × natpair × elem → sparsearray
. [ . ]	matrix	pf	matrix × nat × nat → elem with λ mx, r, c:nat. r < #r mx ∧ c < #c mx
. [ . ]	matrix	pf	matrix × nat × nat × elem → matrix with λ mx, r, c, a. r < #r m ∧ c < #c mx
. [ . ]	matrixops	pf	vector × nat → elem with λ ar, n. n < # ar
. [ . ]	matrixops	pf	vector × nat × elem → vector with λ ar, n, a. n < # ar
. [ . ]	sparsearray	pf	sparsearray × natpair → elem with λ st, a. a ∈ st
. [ . ]c	matrixops	pf	matrix × nat → vector with λ mx, c. c < #c mx
. [ . ]r	matrixops	pf	matrix × nat → vector with λ mx, r. r < #r mx
. \ .	natset	f	natset × natset → natset
. \ .	sparsearray	f	npset × npset → npset
. \ .	sparsearray	f	sparsearray × npset → sparsearray
. \| .	sparsearray	f	sparsearray × npset → sparsearray
. × .	natpair	f	nat × nat → natpair
. ∈ .	natset	p	nat × natset
. ∈ .	sparsearray	p	natpair × sparsearray
. ∈ .	sparsearray	p	natpair × npset
. ∈ .	sparsearray	p	elem × sparsearray
. ∩ .	natset	f	natset × natset → natset
. ∩ .	sparsearray	f	npset × npset → npset
. ∪ .	natset	f	natset × natset → natset
. ∪ .	sparsearray	f	npset × npset → npset
. ≤ .	nat	p	nat × nat
. ≥ .	nat	p	nat × nat
. ⊆ .	natset	p	natset × natset
. ⊆ .	sparsearray	p	sparsearray × sparsearray
. ⊆ .	sparsearray	p	npset × npset
. ⊕ .	sparsearray	f	sparsearray × sparsearray → sparsearray
. to .	natset	f	nat × nat → natset
{ . }	natset	f	nat → natset
{ . }	sparsearray	f	natpair → npset
Σ	matrixops	f	natset × (nat → elem) → elem
∅	natset	c	natset
∅	sparsearray	c	sparsearray
∅	sparsearray	c	npset
I	ring	c	elem
MULT#	VerifyThis3-sequential	pr	sparsearray × nat × vector : : vector (nondeterministic)
O	ring	c	elem
O- .	ring	f	elem → elem
O- .	matrixops	f	matrix → matrix
O- .	matrixops	f	vector → vector
a	VerifyThis3-sequential	v	elem
c	VerifyThis3-sequential	v	nat
dom .	sparsearray	f	sparsearray → npset
elem	elem	s
m	VerifyThis3-sequential	v	nat
matrix	matrix	s
mkmatrix	matrix	f	nat × nat × elem → matrix
mkvector	matrixops	f	nat → vector
n	VerifyThis3-sequential	v	nat
nat	nat-basic	s
natpair	natpair	s
natset	natset	s
np	VerifyThis3-sequential	v	natpair
npset	sparsearray	s
okspmx	VerifyThis3-sequential	p	sparsearray × nat × nat
r	VerifyThis3-sequential	v	nat
sparsearray	sparsearray	s
spmx	VerifyThis3-sequential	v	sparsearray
vector	matrixops	s
x	VerifyThis3-sequential	v	vector
y	VerifyThis3-sequential	v	vector