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Proof step 64 from proof uint2bits-mod2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 65:
0 ≤ i, 0 < j ⊦ uint2bits(j * 2 ^ i) = uint2bits(j) + mklist(false, i→n(i))
Proof step 66:
0 ≤ i0 ∧ 0 < i2, false ' = sgn(false ' + lastn(i→n(i0), (uint2bits(i2) + mklist(false, i→n(i0))).rest)), 0 ≤ i0, 0 < 2 ^ i0, 1 < i2, 0 ≤ 2 ^ i0, 0 < i2, 0 ≤ i2, ∀ j0, i. i→n(j0) < i→n((i2 * 2 ^ i0 + 0) * 2 + 0) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, false ' = sgn(false ' + lastn(i→n(i0), (uint2bits(i2) + mklist(false, i→n(i0))).rest) + false ')

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 → (j ≤ i ↔ i = j);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward) Used terms: i0, i2