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Proof step 14 from proof int2int-inj (previous step)

i < 0, sgn(bitsinvert(uint2bits(~ i)) +1).first ⊦ bits2uint((false ' + bitsinvert(sgn(bitsinvert(uint2bits(~ i)) +1).rest))+1) + i = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 15:
0 < i ⊦ ∃ bits. uint2bits(i) = false ' + true ' + bits
Proof step 16:
∃ bits. uint2bits(~ i) = false ' + true ' + bits, i < 0, sgn(bitsinvert(uint2bits(~ i)) +1).first ⊦ bits2uint((false ' + bitsinvert(sgn(bitsinvert(uint2bits(~ i)) +1).rest))+1) + i = 0

Rule argument

name: uint2bits-expos0 subst: [i] → [~ i]

Additional information

Used simplifier rules: ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: ~ i