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Proof step 18 from proof eq-one (previous step)

i * j = 1, j ≤ 0, i < 0 ⊦ i = 0, ~1 = j ∧ i = ~1

User applied rule insert lemma

And obtained the following new goals

Proof step 19:
0 < i, 0 < j, i ≤ i0, j < j0 ⊦ i * j < i0 * j0
Proof step 20:
i * j = 1, j ≤ 0, i < 0 ⊦ 0 < 1 ∧ 0 < 1 ∧ 1 ≤ ~ i ∧ 1 < ~ j, i = 0, ~1 = j ∧ i = ~1

Rule argument

spec: int-mult inst: name: pls-pos seq: 0 < i, 0 < j, i ≤ i0, j < j0 ⊦ i * j < i0 * j0 subst: [i, j, i0, j0] → [1, 1, ~ i, ~ j] flags: current, []

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%minus-left: ⊦ ~ i * j = ~(i * j);%neg-02: ⊦ ~ ~ i = i; from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs Used terms: 1, 1, ~ i, ~ j