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Theorem mult-com
- 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,
commutativity,
eq-dist,
eq-neg-01,
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-neg-01,
ls-pos,
ls-pos-01,
ls-pos-02,
ls-same,
ls-same-01,
ls-same-02,
ls-same-03,
ls-same-04,
ls-same-05,
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