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Proof step 47 from proof int2bytes-first-zerobyte (previous step)

9 < # int2bits(i % 256), 256 ≤ i, 0 ≤ i, 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 ≤ i0 → (int2bytes(i0).first = i2b(0) ↔ n→i(# int2bits(i0)) % 8 = 1) ⊦ n→i(# fillsgn(9, int2bits(i % 256)) - 1) % 8 = 0, int2bytes(i / 256).first = i2b(0) ↔ (n→i(# fillsgn(9, int2bits(i % 256)) - 1) + n→i(# int2bits(i / 256))) % 8 = 1, fillsgn(9, int2bits(i % 256)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1)) subst: [i, m] → [i % 256, 9] rotate: F spec: int2bits inst: name: int2bits-lslen-06

Additional information

Used simplifier rules: ⊦ j > 0 → i % j < j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i ∧ 0 < j → (i % j ≤ 0 ↔ i % j = 0);% ⊦ m < n → n ≠ 0; (forward)% ⊦ int2bits(0) = false ';% ⊦ # boolvar ' = 0 +1;% ⊦ 0 < n → fillsgn(n, boolvar ') = mklist(boolvar, n);%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n; Used terms: i % 256, 9