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Proof step 3 from proof bor-shift-plus (previous step)

0 ≤ i ∧ i < 32 ⊦ j0 < 2 ^ i ∧ 0 ≤ j0 ∧ 0 ≤ i ∧ i < 32 → bor(j * 2 ^ i, j0) = j * 2 ^ i + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ j0 < 2 ^ i ∧ 0 ≤ i ∧ 0 ≤ j0 ∧ 0 ≤ j → bor(j * 2 ^ i, j0) = j * 2 ^ i + j0
Proof step 5:
¬(j0 < 2 ^ i ∧ 0 ≤ i ∧ 0 ≤ j0 ∧ 0 ≤ j), 0 ≤ i ∧ i < 32 ⊦ j0 < 2 ^ i ∧ 0 ≤ j0 ∧ 0 ≤ i ∧ i < 32 → bor(j * 2 ^ i, j0) = j * 2 ^ i + j0

Rule argument

name: bor-2pot-plus rotate: F subst: [j0, i, j] → [j0, i, j]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: j0, i, j