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Theorem distr
⊦ r * (r0 + r1) = r * r0 + r * r1
Type: An axiom
Validity: The proof is valid.
Features: ls,
Comment: used as local simprule only
Used by:
eq-dist
,
eq-nonzero
,
eq-succ
,
eq-succ-01
,
invmult-ge-neg-add
,
invmult-ge-pos-add
,
invmult-gr-neg-add
,
invmult-gr-pos-add
,
invmult-le-neg-add
,
invmult-le-pos-add
,
invmult-ls-neg-add
,
invmult-ls-pos-add
,
le-dist
,
le-dist-01
,
le-dist-02
,
le-neg
,
le-pos
,
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-neg
,
ls-pos
,
minus-left
,
minus-one
,
mult-add-greater
,
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
,
square-eq-01
,
square-eq-02
,
square-eq-03
,
square-interval
,
square-interval-01
,
square-le-04
,
square-le-05
,
square-le-05a
,
square-ls-02
,
square-ls-03
,
square-ls-03a
,
square-ls-04
,
square-ls-04a
,
square-zero-01
,
square-zero-01a
,
square-zero-02
,
succ-lsplit
,
succ-rmerge
,
succ-rsplit
,
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-03
,
two-sub-04
,
two-sub-05
,
zero-ge-add-02
,
Used by units in proved state:
Proof exists?: No