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Proof step 3 from proof modeqp-02 (previous step)

i * j + j0 = i0 * j + j1, j < 0, j0 + j < 0, j1 + j < 0, 0 ≤ j0, 0 ≤ j1 ⊦ i = i0 ∧ j0 = j1

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> 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] → [i, ~ j, j1, i0, j0]

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i + ~ j = i - j; (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 = i0 ↔ i = i0 + j; (s)% ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ i < ~ j ↔ i + j < 0; (s) Used terms: i, ~ j, j1, i0, j0