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Proof step 34 from proof longin-mult-01 (previous step)

~2147483648 ≤ j, i < 0, j < 0, j < ~2147483647, 9223372036854775807 < i * j, ~2147483648 < i ⊦ j = 0, ~2147483648 = i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: ls-rew-succ seq: ⊦ i < j ↔ i + 1 ≤ j subst: [j, i] → [~2147483647, j] flags: rewrite

Additional information

Used simplifier rules: numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%numlsneg-03: i < 0 ⊦ j < (* i) * i0 ↔ ~ i * i0 + j < 0; from specification int-mult%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%nummult-ls-01: ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i); from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lst: ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; from specification int-basic1 Used terms: ~2147483647, j