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Proof step 7 from proof zero-gr-add-02 (previous step)

i1 * j + i1 = i1 * (j + 1), 0 < i1 * j + i1, i1 * j + i0 ≤ i1 * j + i1, 0 ≤ i0, 0 < i1 * j + i0, i0 ≤ i1, j + 1 < i1 * j + i0, j < i1 * j + i0, j < 0, 0 < i1, j + 1 < i1 ⊦ i1 = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); 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