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Theorem modex

j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: div-add-both, div-add-nosucc, div-div-switch, div-le-modzero, div-ls, div-ls-modzero, div-minus-onediff-01, div-mult-num, div-sub-01, div-two-intro, even-add, even-mult, mod-add-both-zero, mod-mod-less, mod-next-square, mod-zero-num, modmod-add-zero, nummult-eq-01, nummult-modle-01, nummult-modls-01,
Used by units in proved state: int-pot, int-gcd, int-square, int-min,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 10
Used lemmas: div-elim3, mod-ls-same-02, mod-pos-not-neg, div-elim2, div-elim1, div-elim-pos, mod-mult-04,
Used spec theorems:
- int-abs/le-def
Used simplifier rules: