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Proof step 22 from proof less-mult-div-01 (previous step)

i2 * i + j0 = 0, 0 < j1, j0 < i1 + i2, 0 ≤ j0, 0 < i1, 0 < i2, 1 < i1 + i2, 0 < i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 inst: name: zero-06 seq: ⊦ ¬ i < 0 ∧ ¬ j < 0 → (0 = i + j ↔ i = 0 ∧ j = 0) subst: [j, i] → [j0, i2 * i] flags: rewrite

Additional information

Used simplifier rules: zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 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%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: j0, i2 * i