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Proof step 13 from proof bits2int-split-01 (previous step)

true ∈ bits0 ⊦ bitsinvert(bits0) +1 = [], bits0 = [], bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bitsinvert(bits0) +1) = bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ false ∈ bits → # bits +1 = # bits

Rule argument

seq: ⊦ false ∈ bits → # bits +1 = # bits subst: [bits] → [bitsinvert(bits0)] rotate: F spec: bitopsaux inst: name: succ-len

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ # bitsinvert(bits) = # bits;% ⊦ ¬ false ∈ bits → bits +1 = true + bitsinvert(bits);% ⊦ bitsinvert(bitsinvert(bits)) = bits;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ false ∈ bitsinvert(bits) ↔ true ∈ bits; Used terms: bitsinvert(bits0)