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Proof step 2 from proof mod-two-ge-01 (previous step)

j < i, 0 ≤ j ⊦ (2 ^ i - 1) % 2 ^ j = 2 ^ j - 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
j ≠ 0 ⊦ i % j = i - i / j * j
Proof step 4:
j < i, 0 ≤ j ⊦ 2 ^ i - 1 - (2 ^ i - 1) / 2 ^ j * 2 ^ j = 2 ^ j - 1, 2 ^ j = 0

Rule argument

spec: int-div name: mod-rew seq: j ≠ 0 ⊦ i % j = i - i / j * j subst: [j, i] → [2 ^ j, 2 ^ i - 1] flags: <all paths>

Additional information

Used simplifier rules: two-zero: ⊦ 0 ≤ j → 2 ^ j ≠ 0; Used terms: 2 ^ j, 2 ^ i - 1