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Proof step 2 from proof succ-length (previous step)

# bits + 1 < # bitsinvert(bits) +1 ⊦ bitsinvert(bits) +1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ false ∈ bits → # bits +1 = # bits

Rule argument

name: succ-len rotate: F subst: [bits] → [bitsinvert(bits)]

Additional information

Used simplifier rules: succ-ones: ⊦ ¬ false ∈ bits → bits +1 = true + bitsinvert(bits);%inv-inv: ⊦ bitsinvert(bitsinvert(bits)) = bits;%inv-in-01: ⊦ false ∈ bitsinvert(bits) ↔ true ∈ bits;%inv-len: ⊦ # bitsinvert(bits) = # bits;% ⊦ ¬ m + n < m;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bitsinvert(bits)