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Proof step 16 from proof uint2bits-div2pot (previous step)

j / 2 < 2 ^ i0, 0 < j, 2 ^ (i0 + 1) ≤ j, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i ≤ j0 → uint2bits(j0 / 2 ^ i) = butlastn(i→n(i), uint2bits(j0)) ⊦ j = 1, uint2bits(j / 2 ^ (i0 + 1)) = butlastn(i→n(i0), uint2bits(j / 2)), ~1 = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
0 < j, 0 ≤ i, i < j ⊦ i / j = 0
Proof step 18:
¬(0 < 2 ^ (i0 + 1) ∧ 0 ≤ j ∧ j < 2 ^ (i0 + 1)), j / 2 < 2 ^ i0, 0 < j, 2 ^ (i0 + 1) ≤ j, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i ≤ j0 → uint2bits(j0 / 2 ^ i) = butlastn(i→n(i), uint2bits(j0)) ⊦ j = 1, uint2bits(j / 2 ^ (i0 + 1)) = butlastn(i→n(i0), uint2bits(j / 2)), ~1 = i0

Rule argument

seq: 0 < j, 0 ≤ i, i < j ⊦ i / j = 0 subst: [j, i] → [2 ^ (i0 + 1), j] rotate: F spec: int-div inst: name: div-zero

Additional information

Used simplifier rules: uint2bits-zero: ⊦ uint2bits(0) = false ';% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 2 ^ (i0 + 1), j