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Proof step 19 from proof int2int-lastn-pospos (previous step)

bits = boolvar + bits0, i = bits2uint(lastn(m, int2bits(i))) + 2 ^ n→i(m) * bits2uint(bits), int2bits(i) = bits + lastn(m, int2bits(i)), # bits = # int2bits(i) - m, m ≤ # int2bits(i), 0 < i ⊦ m = 0, bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m), bits = [], boolvar, lastn(m, int2bits(i)).first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
1 + # bits0 = # int2bits(i) - m, int2bits(i) = (false ' + bits0) + lastn(m, int2bits(i)), i = bits2uint(bits0) * 2 ^ n→i(m) + bits2uint(lastn(m, int2bits(i))), false ∈ int2bits(i), 0 < i, m ≤ # int2bits(i) ⊦ bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m), m = 0, lastn(m, int2bits(i)).first

Rule argument

Additional information

Used simplifier rules: bits2uint-zeros-03: ⊦ bits2uint(false ' + bits) = bits2uint(bits);% ⊦ i < j ∧ j = i0 → i < i0; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar ' + bits ≠ [];% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar + bits = boolvar ' + bits;