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Proof step 12 from proof int2bits-truein-01 (previous step)

int2bits(j) = true ' + bits, j < 0 ⊦ j = 0, true ∈ bits, ∃ i. ¬ i < 0 ∧ 2 ^ i + j = 0

User applied rule cut formula

And obtained the following new goals

Proof step 13:
bits2int(int2bits(j)) = bits2int(true ' + bits), int2bits(j) = true ' + bits, j < 0 ⊦ j = 0, true ∈ bits, ∃ i. ¬ i < 0 ∧ 2 ^ i + j = 0
Proof step 17:
int2bits(j) = true ' + bits, j < 0 ⊦ bits2int(int2bits(j)) = bits2int(true ' + bits), j = 0, true ∈ bits, ∃ i. ¬ i < 0 ∧ 2 ^ i + j = 0

Rule argument

fma: bits2int(int2bits(j)) = bits2int(true ' + bits)

Additional information

Used formulas: bits2int(int2bits(j)) = bits2int(true ' + bits)