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Proof step 16 from proof mod-pred-neg (previous step)

i0 * j + j0 = 1 + i2 * j, i2 < 0, i2 < j, i2 * j < ~1, abs(j0) < j, i0 < j, j0 < j, 0 < j, 0 < j + j0, i2 < j + j0, i0 < j + j0, i0 ≤ 0, j0 ≤ 0 ⊦ 1 = j0 + j, j0 = 1

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i0, j, 0, i2, 1 - j0]

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i + j = i + i0 ↔ j = i0; (s)% ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0); (s)% ⊦ i - j < i0 ↔ i < j + i0; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)% ⊦ i < 1 ↔ i ≤ 0; (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: i0, j, 0, i2, 1 - j0