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Proof step 11 from proof nummult-ls-03 (previous step)

j + 1 = i2 + i1, i1 < 0, j < 0, i1 ≤ j, i2 ≤ 0 ⊦ j < i2 * i0 ↔ i1 / i2 < i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs name: add-shift seq: ⊦ i + j = i0 ↔ i = i0 - j subst: [i0, j, i] → [i2 + i1, 1, j] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i - j < i0 ↔ i < j + i0; (s)% ⊦ i < j + 1 ↔ i ≤ j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ i + j ≤ i0 + j ↔ i ≤ i0; (s)% ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ i ≤ j → ¬ j < i; (s) Used terms: i2 + i1, 1, j