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Proof step 7 from proof ls-add (previous step)

0 < j, j1 < j, i0 * j + j1 < j, 0 ≤ j1, i0 ≤ 1 ⊦ i0 ≤ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [1, i0] flags: <all paths>

Additional information

Used simplifier rules: one-01: ⊦ i = 1 → i * j = j;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s)% ⊦ i + j < j ↔ i < 0; (s)% ⊦ i ≤ j → ¬ j < i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: 1, i0