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Proof step 42 from proof uint2bits-mod2pot (previous step)

false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i2 * 2 ^ i0).rest)), 0 ≤ i0, 0 < 2 ^ i0, 0 < i2, ∀ j0, i. i→n(j0) < i→n((i2 * 2 ^ i0 + 0) * 2 + 1) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ i2 = 0, ~1 = i0, false ' + true ' = sgn(false ' + lastn(i→n(i0), uint2bits(i2 * 2 ^ i0).rest) + true ')

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: uint2bits-2pot-01 rotate: F subst: [i, j] → [i0, i2]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: i0, i2