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Proof step 12 from proof ex-modeq-half (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 0 ≤ i % j → i |%| j = i % j
Proof step 14:
¬ 0 ≤ i0 % j, odd(j), 0 < j, j / 2 < abs(i0 |%| j), i0 |%| j < j ⊦ ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2, (i0 |%| j - j) |%| j = i0 |%| j ∧ j ≤ i0 |%| j + j / 2
Proof step 26:
0 ≤ i0 % j, odd(j), 0 < j, j / 2 < abs(i0 % j), i0 % j < j ⊦ ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2, (i0 % j - j) |%| j = i0 % j ∧ j ≤ i0 % j + j / 2

Rule argument

spec: inst: name: mod-pos-def seq: ⊦ 0 ≤ i % j → i |%| j = i % j subst: [j, i] → [j, i0] flags: rewrite, current

Additional information

Used terms: j, i0