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Proof step 42 from proof bits2int-lasteq (previous step)

⊦ bits0 = [], 1 + 2 * bits2uint(bits1) = bits2int(bits0 + true ') ↔ bits2uint(bits1) = bits2int(bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ boolvar ∧ ¬ bits.first ∧ bits ≠ [] → bits2int(bits + boolvar ') = bits2int(bits) * 2 + 1
Proof step 44:
¬(true ∧ ¬ bits0.first ∧ bits0 ≠ []) ⊦ bits0 = [], 1 + 2 * bits2uint(bits1) = bits2int(bits0 + true ') ↔ bits2uint(bits1) = bits2int(bits0)

Rule argument

name: bits2int-rec rotate: F subst: [boolvar, bits] → [true, bits0]

Additional information

Used simplifier rules: ⊦ i + j = i + i0 ↔ j = i0;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: true, bits0