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Proof step 7 from proof gcd-negone-eq (previous step)

0 ≤ gcd(i2, j2), ~1 = j2 / gcd(i2, j2) ⊦ 1 = ~ j2 / gcd(i2, j2), j2 + gcd(i2, j2) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: num-neg seq: j ≠ 0 ⊦ i < 0 → (* i) / j = ~(~ i / j) subst: [j, i] → [gcd(i2, j2), j2] flags: rewrite

Additional information

Used simplifier rules: gcd-zero-zero: ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%gcd-zero: ⊦ gcd(0, 0) = 0;%neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j); from specification int-div%neg-02: ⊦ ~ ~ i = i; from specification int-abs%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs Used terms: gcd(i2, j2), j2