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Proof step 5 from proof mod-add-zero (previous step)

j * i1 ≥ 0, i % j + j * i1 = 0, 0 ≤ i, 0 < j, 0 < i1 ⊦ i1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%ge-def: ⊦ i ≥ j ↔ ¬ i < j; from specification int-abs