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Proof step 2 from proof longin-mult-01 (previous step)

~2147483648 ≤ i, i ≤ 2147483647, ~2147483648 ≤ j, j ≤ 2147483647 ⊦ (i * j)∈long

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i ∈long ↔ ~(2 ^ 63) ≤ i ∧ i ≤ 2 ^ 63 - 1
Proof step 4:
~2147483648 ≤ i, i ≤ 2147483647, ~2147483648 ≤ j, j ≤ 2147483647 ⊦ ~(2 ^ 63) ≤ i * j ∧ i * j ≤ 2 ^ 63 - 1

Rule argument

spec: inst: name: inlong seq: ⊦ i ∈long ↔ ~(2 ^ 63) ≤ i ∧ i ≤ 2 ^ 63 - 1 subst: [i] → [i * j] flags: rewrite, current

Additional information

Used terms: i * j