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Theorem mod-neg-01

j ≠ 0 ⊦ ~ i % j = ~(i % j)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: abs-shift, abs-shift-01, div-add-nosucc-neg, div-add-succ-neg, div-elim2, div-elim3, div-twoodd-01, div2-odd-01, ls-even-01, mod-div-zero, mod-mult-neg, mod-rec-01, mod-sub, mod-sub-01, mod-two-pred-02, mod-twoodd-03, mod2-add-neg, modeq-pos-04, modmod-add-02, modmod-mult-02, modmod-mult-03, modmod-mult-07, modnum-neg,
Used by units in proved state: int-pot,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas: divmod-rew, Div-left, mod-rew,
Used spec theorems:
- Used simplifier rules: