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Proof step 4 from proof band-011x-neg-04 (previous step)

0 ≤ i ⊦ band(~ ~ j, i) = band((i + 1) + ~ ~ j, i), false ∈ int2bits(i).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(~ j, i) = band(i + 1 - j, i)

Rule argument

name: band-011x-neg-03 rotate: F subst: [i, j] → [i, ~ j]

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - ~ j = i + j;% ⊦ ~ ~ i = i; Used terms: i, ~ j