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Proof step 18 from proof ls-def (previous step)

i * j0 = i1 + i0 * j, 0 < j, 0 < j0, i * j0 < i0 * j, 0 ≤ i1 ⊦ j0 = 0, j = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j < j ↔ i < 0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;