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Proof step 22 from proof int2bytes-len-le (previous step)

b2i(int2bytes(i).first) ≤ 0, 0 ≤ i, 2 ^ (8 * n→i(# int2bytes(i) - 1)) ≤ i, # int2bytes(i) < n, 2 ^ ((n→i(n) - 1) * 8) ≤ i ⊦ int2bytes(i).first = i2b(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ i ≠ j → (i ≤ j ↔ i < j)

Rule argument

seq: ⊦ i ≠ j → (i ≤ j ↔ i < j) subst: [j, i] → [0, b2i(int2bytes(i).first)] rotate: F spec: int-abs inst: name: lels-02

Additional information

Used simplifier rules: bytes2int-first-lez: ⊦ b2i(int2bytes(i).first) < 0 ↔ i < 0;% ⊦ b2i(by) = i → (i2b(i) ≠ by ↔ false);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 0, b2i(int2bytes(i).first)