[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. 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
,
Theorem mult-ass
⊦ (r * r0) * r1 = r * r0 * r1
Type: An axiom
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
abs-eqall
,
abs-eqneg
,
abs-le-one-multiple
,
abs-ls-multiple-one
,
abs-ls-one-multiple
,
abs-ls-same
,
abs-not-neg
,
add-mult-two
,
eq-dist
,
eq-nonzero
,
eq-nonzero-01
,
eq-nonzero-02
,
eq-nonzero-03
,
eq-pos-01
,
eq-same
,
eq-same-01
,
eq-same-02
,
eq-same-03
,
eq-succ
,
eq-succ-01
,
est-nle
,
inv-eq
,
inv-le-neg
,
inv-le-pos
,
inv-ls-neg
,
inv-ls-pos
,
inv-mult
,
inv-mult-add-eq
,
inv-twice
,
invmult-eq
,
invmult-ge-neg
,
invmult-ge-neg-add
,
invmult-ge-pos
,
invmult-ge-pos-add
,
invmult-gr-neg
,
invmult-gr-neg-add
,
invmult-gr-pos
,
invmult-gr-pos-add
,
invmult-le-neg
,
invmult-le-neg-add
,
invmult-le-pos
,
invmult-le-pos-add
,
invmult-ls-neg
,
invmult-ls-neg-add
,
invmult-ls-pos
,
invmult-ls-pos-add
,
le-abs
,
le-dist
,
le-dist-01
,
le-dist-02
,
le-neg
,
le-neg-01
,
le-pos
,
le-pos-01
,
le-same
,
le-same-01
,
le-same-02
,
le-same-03
,
le-same-04
,
le-same-05
,
le-same-06
,
ls-add-02
,
ls-add-03
,
ls-dist
,
ls-dist-01
,
ls-dist-02
,
ls-dist-03
,
ls-dist-04
,
ls-dist-05
,
ls-dist-06
,
ls-forward
,
ls-neg
,
ls-pos
,
ls-pos-01
,
ls-pos-02
,
ls-same
,
ls-same-01
,
ls-same-02
,
ls-same-03
,
ls-same-04
,
ls-two
,
ls-two-01
,
ls-two-02
,
ls-two-03
,
minus-left
,
minus-one
,
minus-one-01
,
mods-ls
,
mods-zero-07
,
mult-add-greater
,
mult-gt-both
,
mult-gt-one
,
mult-pos
,
mult-pos-pos
,
mult-zero
,
neq-not-zero
,
neq-not-zero-01
,
noeth-zero-ls
,
num-distr
,
num-distr-add-eq1
,
num-distr-add-eq2
,
num-distr-add-le1
,
num-distr-add-le2
,
num-distr-add-ls1
,
num-distr-add-ls2
,
num-distr-addboth-eq1
,
num-distr-addboth-eq2
,
num-distr-addboth-le1
,
num-distr-addboth-le2
,
num-distr-addboth-ls1
,
num-distr-addboth-ls2
,
num-distr-eq1
,
num-distr-eq2
,
num-distr-le1
,
num-distr-le2
,
num-distr-ls1
,
num-distr-ls2
,
ple-neg
,
ple-pos
,
ple-pos-better
,
pls-neg
,
pls-pos
,
pls-pos-01
,
pls-pos-02
,
pnle-neg
,
pnle-pos
,
pnls-neg
,
pnls-negpos
,
pnls-pos
,
pnls-posneg
,
posint-factor
,
pzero-gr
,
pzero-ls
,
square-abs
,
square-eq-01
,
square-eq-02
,
square-eq-03
,
square-eq-one
,
square-ge-one
,
square-gez
,
square-gez-01
,
square-gr-one
,
square-interval
,
square-interval-01
,
square-le
,
square-le-03
,
square-le-04
,
square-le-05
,
square-le-05a
,
square-le-one
,
square-lez
,
square-lez-01
,
square-ls-01
,
square-ls-02
,
square-ls-03
,
square-ls-03a
,
square-ls-04
,
square-ls-04a
,
square-ls-one
,
square-minus
,
square-zero
,
square-zero-01
,
square-zero-01a
,
square-zero-02
,
succ-lsplit
,
succ-rmerge
,
succ-rsplit
,
twice-le-zero
,
twice-ls-zero
,
two-eq
,
two-le
,
two-le-01
,
two-le-02
,
two-le-03
,
two-le-04
,
two-ls
,
two-ls-01
,
two-ls-02
,
two-ls-03
,
two-ls-04
,
two-sub
,
two-sub-01
,
two-sub-02
,
two-sub-03
,
two-sub-04
,
two-sub-05
,
zero-eq
,
zero-ge
,
zero-ge-01
,
zero-ge-02
,
zero-ge-03
,
zero-ge-add-01
,
zero-ge-add-02
,
zero-ge-case
,
zero-gr
,
zero-gr-01
,
zero-gr-02
,
zero-gr-03
,
zero-gr-add-01
,
zero-gr-case
,
zero-le
,
zero-le-01
,
zero-le-02
,
zero-le-03
,
zero-le-case
,
zero-left
,
zero-ls
,
zero-ls-01
,
zero-ls-02
,
zero-ls-03
,
zero-ls-case
,
zero-neq
,
zero-neq-01
,
Used by units in proved state:
real-limit
,
Proof exists?: No