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Proof step 22 from proof int2uint-neg (previous step)

true ∈ uint2bits(~ j).rest.rest, j < 0 ⊦ 2 ^ n→i(# uint2bits(~ j)) = 2 ^ n→i(# bitsinvert(uint2bits(~ j)) +1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ false ∈ bits → # bits +1 = # bits

Rule argument

seq: ⊦ false ∈ bits → # bits +1 = # bits subst: [bits] → [bitsinvert(uint2bits(~ j))] rotate: F spec: bitopsaux inst: name: succ-len

Additional information

Used simplifier rules: uint2bits-onein-01: ⊦ j < 0 → true ∈ uint2bits(~ j);% ⊦ # bitsinvert(bits) = # bits;% ⊦ ¬ false ∈ bits → bits +1 = true + bitsinvert(bits);% ⊦ bitsinvert(bitsinvert(bits)) = bits;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 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(uint2bits(~ j))