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Proof step 4 from proof congmod-def-mod-02 (previous step)

i < 0, i0 < 0 ⊦ ≡mod(i, i0, abs(j)) ↔ i |%| j = i0 |%| j, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j)
Proof step 6:
0 < abs(j), i < 0, i0 < 0 ⊦ i |%| abs(j) = i0 |%| abs(j) ↔ i |%| j = i0 |%| j, j = 0

Rule argument

spec: int-mod inst: name: congmod-def-mod seq: ⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j) subst: [j, i0, i] → [abs(j), i0, i] flags: rewrite, current

Additional information

Used simplifier rules: abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs Used terms: abs(j), i0, i