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Proof step 5 from proof mod-nle (previous step)

j * i + i0 - j = j * (i - 1) + i0, i0 < i, 0 < j, 0 < i, j * i + i0 - j ≤ 0, j * i + i0 ≤ j, 0 ≤ i0 ⊦ i = 1 ∧ i0 = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: zero-le: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs% ⊦ i + j ≤ i ↔ j ≤ 0; (s)% ⊦ i - j ≤ i0 ↔ i ≤ j + i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1