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Proof step 37 from proof int2bytes-len-ls-01 (previous step)

# int2bits(i) / 8 = i→n(i0), i→n(8 * i0 - 1) + 1 < # int2bits(i), 0 < i0, 0 < i, i < 2 ^ (8 * i0) ⊦ # int2bits(i) % 8 = 0, i = 0, n ≤ i→n(i0) ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1), i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
0 ≤ i ⊦ (* m) ≤ i→n(i) ↔ n→i(m) ≤ i
Proof step 39:
0 ≤ i0, # int2bits(i) / 8 = i→n(i0), i→n(8 * i0 - 1) + 1 < # int2bits(i), 0 < i0, 0 < i, i < 2 ^ (8 * i0) ⊦ # int2bits(i) % 8 = 0, i = 0, n→i(n) ≤ i0 ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1), i0 = 0

Rule argument

seq: 0 ≤ i ⊦ (* m) ≤ i→n(i) ↔ n→i(m) ≤ i subst: [i, m] → [i0, n] rotate: F spec: intnat inst: name: num-i2n-le-02

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i < j ↔ j ≤ i; Used terms: i0, n