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Proof step 25 from proof bits2bytes-mklist-02 (previous step)

8 < n0 * 8, ∀ n1. n1 < n0 * 8 → n1 % 8 = 0 → n1 = 0 ∨ bits2bytes(mklist(true, n1)) = mklist(i2b(~1), n1 / 8) ⊦ n0 = 0, bits2bytes(mklist(true, n0 * 8 - 8)) + i2b(bits2int(true ' + true ' + true ' + true ' + true ' + true ' + true ' + true ')) ' = mklist(i2b(~1), n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ¬ false ∈ bits ∧ bits ≠ [] → bits2int(bits) = ~1
Proof step 27:
¬ false ∈ true ' + true ' + true ' + true ' + true ' + true ' + true ' + true ' ∧ true ' + true ' + true ' + true ' + true ' + true ' + true ' + true ' ≠ [], 8 < n0 * 8, ∀ n1. n1 < n0 * 8 → n1 % 8 = 0 → n1 = 0 ∨ bits2bytes(mklist(true, n1)) = mklist(i2b(~1), n1 / 8) ⊦ n0 = 0, bits2bytes(mklist(true, n0 * 8 - 8)) + i2b(~1) ' = mklist(i2b(~1), n0)

Rule argument

seq: ⊦ ¬ false ∈ bits ∧ bits ≠ [] → bits2int(bits) = ~1 subst: [bits] → [ true ' + true ' + true ' + true ' + true ' + true ' + true ' + true '] rotate: F spec: int2bits inst: name: bits2int-ones

Additional information

Used simplifier rules: ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ []; Used terms: true ' + true ' + true ' + true ' + true ' + true ' + true ' + true '