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Proof step 10 from proof bits2int-pos (previous step)

(# bits0 + 1) % 8 = 0, 7 < # bits0 ⊦ 0 ≤ bits2int(bytes2bits(bits2bytes(boolvar ' + bits0))) ↔ ¬ boolvar, bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ # bits % 8 = 0 ∧ bits ≠ [] → bytes2bits(bits2bytes(bits)) = bits
Proof step 12:
#(boolvar ' + bits0) % 8 = 0 ∧ boolvar ' + bits0 ≠ [], (# bits0 + 1) % 8 = 0, 7 < # bits0 ⊦ 0 ≤ bits2int(boolvar ' + bits0) ↔ ¬ boolvar, bits0 = []

Rule argument

name: bits2bits-inj rotate: F subst: [bits] → [boolvar ' + bits0]

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ []; Used terms: boolvar ' + bits0