[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,
Used simplifier rules/spec theorems by specification
Used from specification nat
- nat/sub-succ
is used by
gcd-mod-one,
- nat/add-01
is used by
gcd-mod-one,
- nat/add-num-04
is used by
twodiv-01,
- nat/anti
is used by
prime-smallest,
gcd-zero-01-h,
gcd-le-both-h,
gcd-div-both-h,
gcd-alldiv-h,
- nat/cancel-01
is used by
dist-add-01,
- nat/elim-pred-c
is used by
gcd-conq-one,
divi-two-01,
- nat/elim-sub
is used by
gcdex-dist,
gcd-zero-01-h,
gcd-twicerev,
gcd-twice,
gcd-rec2,
gcd-mult,
gcd-le-both-h,
gcd-div-both-h,
gcd-alldiv-h,
divi-sub,
divi-same,
divi-dist,
dist-snd-01,
dist-mult,
dist-c,
dist-add-01,
cong-equiv,
- nat/eq-01
is used by
gcd-rec2,
gcd-mod,
gcd-add,
dist-c,
dist-add,
cong-equiv,
- nat/eq-02
is used by
gcdexh,
- nat/fle
is used by
not-prime,
gcd-eq,
- nat/fle-01
is used by
not-prime,
modprime,
mod-zero,
gcd-le-both-h,
gcd-eq,
- nat/le-add
is used by
gcd-zero-01-h,
gcd-le-both-h,
gcd-div-both-h,
gcd-alldiv-h,
dist-add,
- nat/le-ls-simp
is used by
gcd-mult,
gcd-le-both-h,
- nat/lels
is used by
gcd-zero-01-h,
gcd-mult,
gcd-mod-one,
gcd-le-both-h,
gcd-le-both,
gcd-div-both-h,
gcd-div-both,
gcd-alldiv-h,
gcd-alldiv,
divi-sub,
divi-add,
dist-c,
dist-add-01,
dist-add,
- nat/lels-01
is used by
prime-smallest,
prime-prime,
not-prime,
modprime,
gcdexh,
gcdex-dist,
gcdex,
gcd-twicerev,
gcd-twice,
gcd-rec2,
gcd-mult,
gcd-mod-one,
gcd-mod,
gcd-max,
gcd-le,
gcd-id,
gcd-eq,
gcd-conq-one,
gcd-add,
divi-same,
divi-dist,
dist-same,
dist-mult,
dist-c,
dist-add-01,
cong-equiv,
- nat/lels-02
is used by
two-01,
prime-smallest,
gcdnex-prime,
gcdexh,
gcd-two,
gcd-le-both,
dist-eq,
- nat/lels-03
is used by
prime-smallest,
not-prime,
gcdex,
gcd-zero-01-h,
gcd-mult,
gcd-le-both-h,
gcd-div-both-h,
gcd-alldiv-h,
divi-same,
divi-dist,
dist-mult,
dist-c,
dist-add-01,
cong-equiv,
- nat/lep
is used by
gcd-rec2,
gcd-mult,
gcd-mod,
divi-sub,
divi-same,
cong-equiv,
- nat/lep-02
is used by
divi-same,
dist-add-01,
- nat/ler
is used by
gcdexh,
gcd-le-both,
gcd-div-both-h,
gcd-div-both,
gcd-alldiv-h,
gcd-alldiv,
- nat/let
is used by
prime-smallest,
prime-prime,
gcdnex-prime,
- nat/lez
is used by
gcdexh,
dist-zero,
- nat/ls-le-simp
is used by
gcd-le,
dist-add-01,
- nat/not-zero
is used by
prime-smallest,
prime-prime,
not-prime,
mult-03,
modprime,
mod-zero,
gcdnex-prime,
gcd-conq-one,
- nat/one-02
is used by
leone,
- nat/sub-base
is used by
dist-zero,
- nat/zero
is used by
gcd-id,
divi-add,
dist-same,
- nat/zero-01
is used by
dist-eq,
- nat/zero-02
is used by
dist-eq,
Used from specification nat-basic2
- nat-basic2/a
is used by
gcdexh,
- nat-basic2/c
is used by
gcdexh,
- nat-basic2/a
is used by
twodiv-02,
twodiv-01,
succ,
prime-smallest,
mult-01,
modprime,
gcdnex-prime,
gcdnex,
gcdexh,
gcdex-dist,
gcd-zero-01-h,
gcd-twicerev,
gcd-twice,
gcd-rec2,
gcd-one,
gcd-mult,
gcd-mod-one,
gcd-mod,
gcd-le-both-h,
gcd-div-both-h,
gcd-conq-one,
gcd-alldiv-h,
gcd-addrev,
gcd-add,
divi-two-03,
divi-two-01,
divi-succ,
divi-sub,
divi-same,
divi-primmult,
divi-mod,
divi-dist,
divi-add-01,
divi-add,
div-multadd,
dist-snd-01,
dist-mult-01,
dist-mult,
dist-c,
dist-add-01,
dist-add,
cong-equiv,
- nat-basic2/add-base
is used by
prime-smallest,
modprime,
divi-sub,
divi-same,
divi-mod,
divi-add,
dist-add,
- nat-basic2/c
is used by
twodiv-02,
twodiv-01,
succ,
prime-smallest,
mult-01,
modprime,
gcdnex-prime,
gcdnex,
gcdexh,
gcdex-dist,
gcd-zero-01-h,
gcd-twicerev,
gcd-twice,
gcd-rec2,
gcd-one,
gcd-mult,
gcd-mod-one,
gcd-mod,
gcd-le-both-h,
gcd-div-both-h,
gcd-conq-one,
gcd-alldiv-h,
gcd-addrev,
gcd-add,
divi-two-03,
divi-two-01,
divi-succ,
divi-sub,
divi-same,
divi-primmult,
divi-mod,
divi-dist,
divi-add-01,
divi-add,
div-multadd,
dist-snd-01,
dist-mult-01,
dist-mult,
dist-c,
dist-add-01,
dist-add,
cong-equiv,
- nat-basic2/eq
is used by
divi-add,
- nat-basic2/eq-01
is used by
gcd-mult,
gcd-conq-one,
divi-two-01,
divi-sub,
divi-same,
cong-equiv,
- nat-basic2/eqs
is used by
gcdex-dist,
- nat-basic2/l
is used by
gcd-mult,
divi-same,
dist-add-01,
- nat-basic2/l-01
is used by
gcd-zero-01-h,
gcd-mult,
gcd-le-both-h,
gcd-div-both-h,
gcd-alldiv-h,
divi-same,
dist-c,
cong-equiv,
- nat-basic2/l-02
is used by
gcdex-dist,
gcd-rec2,
gcd-mod,
gcd-add,
dist-c,
cong-equiv,
- nat-basic2/l-05
is used by
mult-01,
- nat-basic2/nls-fst
is used by
gcd-le-both-h,
- nat-basic2/one
is used by
gcdnex-prime,
gcdnex,
divi-primmult,
- nat-basic2/one-02
is used by
gcdnex,
- nat-basic2/one-03
is used by
twodiv-01,
- nat-basic2/oz
is used by
twodiv-01,
- nat-basic2/succ
is used by
gcd-one,
gcd-mod,
divi-two-03,
- nat-basic2/z
is used by
gcdexh,
gcd-mod-one,
gcd-mod,
cong-equiv,
- nat-basic2/z-01
is used by
gcd-zero-01-h,
gcd-mod-one,
gcd-div-both-h,
gcd-conq-one,
gcd-alldiv-h,
divi-two-01,
divi-add,
Used from specification nat-mult
- nat-mult/dist
is used by
gcdexh,
divi-sub,
divi-same,
dist-mult-01,
- nat-mult/dist-sub
is used by
gcdexh,
gcd-mod-one,
cong-equiv,
- nat-mult/modeq
is used by
gcd-mod-one,
- nat-mult/mult-a
is used by
gcd-div-one,
- nat-mult/mult-c
is used by
gcd-div-one-02,
gcd-div-one,
- nat-mult/numeral-07
is used by
divi-add,
- nat-mult/numeral-08
is used by
divi-add,
- nat-mult/addle
is used by
gcd-mult,
- nat-mult/addle-01
is used by
gcd-mult,
divi-sub,
divi-same,
- nat-mult/coef-04
is used by
gcdexh,
divi-add,
div-multadd,
- nat-mult/coef-17
is used by
gcdexh,
divi-two-01,
- nat-mult/dist
is used by
gcd-mult,
- nat-mult/dist-sub-03
is used by
gcd-mult,
- nat-mult/dist-sub-04
is used by
gcd-mult,
- nat-mult/eq
is used by
gcd-mult,
gcd-mod-one,
divi-add,
- nat-mult/eq-same
is used by
not-prime,
mult-01,
modprime,
gcdexh,
gcd-div-one,
divi-three,
divi-sym,
divi-ref,
divi-eq,
- nat-mult/le
is used by
prime-smallest,
prime-prime,
not-prime,
gcdnex-prime,
gcd-mult,
- nat-mult/le-02
is used by
gcd-mod-one,
- nat-mult/le-05
is used by
not-prime,
- nat-mult/ls
is used by
gcdexh,
gcd-mult,
divi-sub,
divi-same,
cong-equiv,
- nat-mult/ls-01
is used by
gcd-mod-one,
divi-ls,
- nat-mult/ls-02
is used by
not-prime,
- nat-mult/ls-04
is used by
modprime,
mod-zero,
- nat-mult/ls-05
is used by
not-prime,
- nat-mult/ls-08
is used by
gcd-mod-one,
- nat-mult/ls-10
is used by
not-prime,
- nat-mult/mult-a
is used by
twodiv,
prime-smallest,
prime-prime,
not-prime,
mult-03,
mult-02,
mult-01,
mult,
modprime,
mod2,
mod-zero,
gcdnex-prime,
gcdexh,
gcdex-dist,
gcd-twicerev,
gcd-twice,
gcd-multdiv,
gcd-mult,
gcd-mod-one,
gcd-mod,
gcd-le-both-h,
gcd-div-one,
gcd-div-both-h,
gcd-conq-one,
gcd-alldiv-h,
divi-zero-01,
divi-zero,
divi-two-02,
divi-two-01,
divi-two,
divi-trans,
divi-three,
divi-sym,
divi-succ,
divi-sub,
divi-same,
divi-ref,
divi-primmult,
divi-one-01,
divi-one,
divi-mult-01,
divi-mod,
divi-ls,
divi-eq,
divi-add-01,
divi-add,
div-multadd,
dist-mult-01,
dist-mult,
cong-equiv,
- nat-mult/mult-base
is used by
gcdexh,
gcd-mult,
gcd-mod-one,
gcd-mod,
cong-equiv,
- nat-mult/mult-c
is used by
twodiv,
prime-smallest,
prime-prime,
not-prime,
mult-03,
mult-02,
mult-01,
mult,
modprime,
mod2,
mod-zero,
gcdnex-prime,
gcdexh,
gcdex-dist,
gcd-twicerev,
gcd-twice,
gcd-multdiv,
gcd-mult,
gcd-mod-one,
gcd-mod,
gcd-le-both-h,
gcd-div-one,
gcd-div-both-h,
gcd-conq-one,
gcd-alldiv-h,
divi-zero-01,
divi-zero,
divi-two-02,
divi-two-01,
divi-two,
divi-trans,
divi-three,
divi-sym,
divi-succ,
divi-sub,
divi-same,
divi-ref,
divi-primmult,
divi-one-01,
divi-one,
divi-mult-01,
divi-mod,
divi-ls,
divi-eq,
divi-add-01,
divi-add,
div-multadd,
dist-mult-01,
dist-mult,
cong-equiv,
- nat-mult/numeral-25
is used by
gcd-twicerev,
gcd-twice,
- nat-mult/one
is used by
mult-03,
mult-02,
gcdnex-prime,
gcd-twicerev,
gcd-twice,
divi-sym,
divi-succ,
divi-one-01,
divi-one,
- nat-mult/one-01
is used by
prime-smallest,
prime-prime,
mult-01,
modprime,
gcd-conq-one,
divi-two,
divi-sym,
divi-one,
divi-eq,
- nat-mult/one-02
is used by
mult,
- nat-mult/rsucc-02
is used by
gcd-mod-one,
gcd-mod,
divi-two-01,
- nat-mult/square-less
is used by
not-prime,
- nat-mult/sqzero
is used by
not-prime,
- nat-mult/three
is used by
divi-three,
- nat-mult/two-02
is used by
gcd-mult,
gcd-le-both-h,
gcd-div-both-h,
gcd-alldiv-h,
- nat-mult/two-03
is used by
mod-zero,
divi-two-02,
- nat-mult/twoeq
is used by
twodiv,
mod2,
- nat-mult/twole
is used by
gcd-mult,
- nat-mult/twole-02
is used by
gcd-twicerev,
gcd-twice,
- nat-mult/twols
is used by
gcd-twicerev,
gcd-twice,
- nat-mult/zero
is used by
divi-zero-01,
divi-zero,
divi-sub,
divi-same,
divi-add,
- nat-mult/zero-01
is used by
mult,
gcdex-dist,
gcd-conq-one,
divi-same,
divi-add,
- nat-mult/zero-02
is used by
gcd-multdiv,
dist-mult-01,
dist-mult,
- nat-mult/zero-06
is used by
prime-smallest,
prime-prime,
not-prime,
mult-01,
modprime,
mod-zero,
gcdnex-prime,
gcd-le-both-h,
gcd-div-both-h,
gcd-conq-one,
gcd-alldiv-h,
divi-same,
divi-ls,
divi-add,
Used from specification nat-basic1
- nat-basic1/f
is used by
prime-smallest,
not-prime,
mult-01,
modprime,
mod-zero,
lstwo,
gcdexh,
gcdex-dist,
gcdex,
gcd-zero-01-h,
gcd-zero-01,
gcd-mult,
gcd-mod-one,
gcd-mod,
gcd-max,
gcd-le-both-h,
gcd-le-both,
gcd-eq,
gcd-div-both-h,
gcd-alldiv-h,
divi-sub,
divi-same,
divi-ls,
divi-dist,
dist-mult,
dist-eq,
dist-add-01,
cong-equiv,
- nat-basic1/less-1
is used by
cong-equiv,
- nat-basic1/lf-01
is used by
mult-01,
gcd-eq,
- nat-basic1/lf-02
is used by
prime-smallest,
gcdex-dist,
gcd-mod-one,
gcd-le-both-h,
divi-ls,
cong-equiv,
- nat-basic1/ls-02
is used by
gcd-mult,
cong-equiv,
- nat-basic1/ls-03
is used by
gcd-div-both,
gcd-alldiv,
divi-add,
- nat-basic1/neq-01
is used by
not-prime,
gcd-zero-01,
dist-eq,
- nat-basic1/one
is used by
twodiv-02,
twodiv-01,
succ,
rax,
prime-smallest,
prime-prime,
not-prime,
mult-02,
mult-01,
mult,
modprime,
mod-zero,
lstwo,
leone,
gcdnex-prime,
gcdnex,
gcd-mod-one-01,
gcd-mod-one,
gcd-conq-one,
divi-primmult,
div,
- nat-basic1/one-01
is used by
gcd-mod-one,
gcd-conq-one,
- nat-basic1/one-02
is used by
gcd-conq-one,
- nat-basic1/ref-1
is used by
gcd-le,
gcd-id,
gcd-eq,
dist-same,
- nat-basic1/twols-01
is used by
not-prime,
gcd-two,
- nat-basic1/twols-02
is used by
prime-smallest,
prime-prime,
not-prime,
modprime,
lstwo,
- nat-basic1/zero
is used by
prime-smallest,
modprime,
Used from specification nat-div
- nat-div/mod-rew
is used by
gcdexh,
- nat-div/modex
is used by
prime-prime,
mod2,
mod-zero,
gcdnex-prime,
- nat-div/cond
is used by
gcdexh,
- nat-div/cond-01
is used by
gcdexh,
- nat-div/div-elim
is used by
prime-smallest,
modprime,
gcd-mod-one,
gcd-mod,
gcd-conq-one,
divi-mod,
cong-equiv,
- nat-div/mod-le-02
is used by
gcdexh,
- nat-div/mod-ls
is used by
cong-equiv,
- nat-div/mod-mult
is used by
gcd-mod-one,
cong-equiv,
- nat-div/mod-mult-01
is used by
prime-smallest,
modprime,
- nat-div/mod-one
is used by
prime-prime,
- nat-div/mod-one-01
is used by
gcd-mod-one,
- nat-div/mod-zero
is used by
gcdexh,