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Proof step 36 from proof ex-modeq-half (previous step)

i0 % j = j0 * j + j, 0 ≤ i0 % j, j / 2 < i0 % j, 0 < j, odd(j) ⊦ j = 0, (i0 % j - j) |%| j = i0 % j ∧ j ≤ i0 % j + j / 2, ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ j ≤ j0 ∧ 0 < j → i % j ≠ j0
Proof step 38:
¬(j ≤ j0 * j + j ∧ 0 < j), i0 % j = j0 * j + j, 0 ≤ i0 % j, j / 2 < i0 % j, 0 < j, odd(j) ⊦ j = 0, (i0 % j - j) |%| j = i0 % j ∧ j ≤ i0 % j + j / 2, ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2

Rule argument

spec: int-div inst: name: mod-neq-02 seq: ⊦ j ≤ j0 ∧ 0 < j → i % j ≠ j0 subst: [j0, j, i] → [j0 * j + j, j, i0] flags: rewrite

Additional information

Used terms: j0 * j + j, j, i0