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Proof step 7 from proof modlep-03 (previous step)

i1 + j1 < abs(i1), abs(j1) < abs(i1), 0 < j, i0 < i, i1 + j1 < j, abs(j1) < j, j * i + i1 ≤ j * i0, 0 ≤ i1 + j1, j ≤ abs(i1) ⊦ i1 = 0

User applied rule apply lemma

And obtained the following new goals

Proof step 8:
j * i + j0 ≤ j * i0, abs(j0) < j ⊦ i ≤ i0
Proof step 9:
abs(j1) < j, i1 + j1 < j, i0 < i, 0 < j, abs(j1) < abs(i1), i1 + j1 < abs(i1), j ≤ abs(i1), 0 ≤ i1 + j1, j * i + i1 ≤ j * i0 ⊦ i1 = 0, j * (i + 1) + (i1 - j) ≤ j * i0 ∧ abs(i1 - j) < j

Rule argument

spec: <toplevel> name: modlep-02 seq: j * i + j0 ≤ j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i + 1, i1 - j, i0]

Additional information

Used simplifier rules: ⊦ i + 1 ≤ j ↔ i < j; (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: j, i + 1, i1 - j, i0