[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 25 from proof longin-mult-01 (previous step)

0 < i * j, j ≤ 2147483647, ~2147483648 ≤ j, i ≤ 2147483647, ~2147483648 ≤ i, 9223372036854775807 < i * j ⊦ abs(i) * abs(j) ≤ 2147483647 * 2147483647

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
0 ≤ i, 0 ≤ j, i ≤ i0, j ≤ j0 ⊦ i * j ≤ i0 * j0
Proof step 27:
¬(0 ≤ abs(i) ∧ 0 ≤ abs(j) ∧ abs(i) ≤ 2147483647 ∧ abs(j) ≤ 2147483647), 0 < i * j, j ≤ 2147483647, ~2147483648 ≤ j, i ≤ 2147483647, ~2147483648 ≤ i, 9223372036854775807 < i * j ⊦ abs(i) * abs(j) ≤ 2147483647 * 2147483647

Rule argument

spec: int-mult inst: name: ple-pos-better seq: 0 ≤ i, 0 ≤ j, i ≤ i0, j ≤ j0 ⊦ i * j ≤ i0 * j0 subst: [j0, i0, j, i] → [2147483647, 2147483647, abs(j), abs(i)] flags: rewrite

Additional information

Used terms: 2147483647, 2147483647, abs(j), abs(i)