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Theorem associativity

⊦ i * j * j0 = (i * j) * j0

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: 5-not-even, 7-not-even, abs-eqall, abs-eqneg, abs-ls-same, abs-ls-same-01, add-mult-two, auxexdivmod, auxexdivmod-01, dist-lsplit, dist-rmerge, dist-sub-merge, dist-sub-split, eq-dist, eq-neg, eq-nonzero, eq-nonzero-01, eq-nonzero-02, eq-nonzero-03, eq-one, eq-one-neg, eq-pos, eq-pos-01, eq-same, eq-same-01, eq-same-02, eq-same-03, eq-succ, est-nle, ex-two, exdivmod, exdivmodpos, four, le-abs, le-dist, le-dist-01, le-dist-02, le-neg, le-neg-01, le-one, 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, le-two, ls-add, 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-same, ls-same-01, ls-same-02, ls-same-03, ls-same-04, ls-same-05, ls-same-06, ls-sub, ls-two, ls-two-01, ls-two-02, ls-two-03, minus-left, minus-one, minus-one-01, minus-one-02, mod-neq, mod-nle, mod-nls, modeqp, modeqp-02, modeqp-03, modeqp-neg, modlep, modlep-03, modlep-04, modlsp, modlsp-03, modlsp-04, modlsp-06, modneqp, mods-nls, mods-zero-07, modzero, modzero-01, modzero-02, modzero-03, modzero-04, modzero-05, modzero-06, modzero-07, modzero-08, mult-add-greater, mult-gt-both, mult-gt-one, mult-pos, mult-pos-pos, mult-sub-less, mult-sub-lesseq, neq-3-not-even, neq-5-not-even, neq-7-not-even, neq-9-not-even, neq-not-zero, neq-not-zero-01, neq-two, noeth-ls-pos, noeth-modlep, noeth-zero-ls, numabs, numabs-01, numdist, numeq, numeq-01, numeq-02, numeq-03, numeq-04, numle, numle-01, numle-02, numle-03, numle-04, numle-05, numle-06, numle-07, numle-08, numle-09, numle-10, numle-11, numle-12, numle-13, numleneg, numleneg-01, numleneg-02, numleneg-03, numls, numls-01, numls-02, numls-03, numls-04, numls-05, numls-06, numls-07, numls-08, numls-09, numls-10, numls-11, numls-12, numls-13, numlsneg, numlsneg-01, numlsneg-02, numlsneg-03, numsub, numsucc, odd-even, one-01, ple-pos, ple-pos-better, pls-neg, pls-pos, pls-pos-01, pls-pos-02, pnle-pos, pnls-negpos, pnls-pos, pnls-posneg, pred-rmerge, short-mult-max, square-abs, square-eq, square-eq-01, square-even, square-ex, square-gez, square-gez-01, square-gez-02, square-inject, square-interval, square-le, square-le-01, square-le-02, square-le-03, square-le-04, square-le-06, square-lez-01, square-ls, square-ls-01, square-ls-02, square-ls-04, square-minus, square-one-le, square-zero, square-zero-01, square-zero-02, succ-rmerge, three, three-01, two-le, two-le-01, two-le-02, two-le-03, two-le-04, two-leone, two-ls, two-ls-01, two-ls-02, two-ls-03, two-ls-04, two-mone, two-oddeq, two-pred, two-sub, two-sub-01, two-zero, zero-eq, zero-ge, zero-ge-01, zero-ge-02, zero-ge-03, zero-ge-add, 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, zero-gr-add-01, zero-gr-add-02, zero-gr-case, zero-le, zero-le-01, zero-le-02, zero-le-03, zero-le-case, zero-ls, zero-ls-01, zero-ls-02, zero-ls-03, zero-ls-case, zero-ls-sub, zero-ls-two, zero-neq, zero-neq-01,
Used by units in proved state: int-pot, int-gcd, int-div, intnat, int-square, int-pair, int-min,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 10
Used lemmas: commutativity, one, dist-rsplit, Mult-zero,
Used spec theorems:
- Used simplifier rules: