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Proof step 41 from proof int2bits-lslen-07 (previous step)

0 ≤ i, 0 < j, 0 ≤ i, 2 ^ i ≤ j, i→n(i + 2) + 1 < # int2bits(2 ^ (i + 1)) ⊦ 0 = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
0 ≤ i ⊦ int2bits(2 ^ i) = false ' + true ' + mklist(false, i→n(i))
Proof step 43:
0 ≤ i + 1, 0 ≤ i, 0 < j, 0 ≤ i, 2 ^ i ≤ j, i→n(i + 2) + 1 < #(false ' + true ' + mklist(false, i→n(i + 1))) ⊦ 0 = j

Rule argument

name: int2bits-2pot rotate: F subst: [i] → [i + 1]

Additional information

Used simplifier rules: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; Used terms: i + 1