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Proof step 11 from proof one-neg (previous step)

1 = i0 * j + j0, i0 + j < ~1, i0 < 0, j0 + j < 0, 0 ≤ j0, j < j0, i0 < j0, j < 0 ⊦ j = ~1, j = 0

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 12:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 13:
1 = i0 * j + j0, i0 + j < ~1, i0 < 0, j0 + j < 0, 0 ≤ j0, j < j0, i0 < j0, j < 0 ⊦ i0 * ~ j + 1 = 0 * ~ j + j0 ∧ 0 ≤ 1 ∧ 1 < ~ j ∧ j0 < ~ j, j = ~1, j = 0

Rule argument

spec: int-mult inst: 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, 1, 0, j0] flags: []

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2 Used terms: i0, ~ j, 1, 0, j0