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Proof step 5 from proof int2bits-bits2unit-01 (previous step)

i < 0 ⊦ int2bits(bits2uint(sgn(bitsinvert(uint2bits(~ i)) +1))) = sgn(false ' + sgn(bitsinvert(uint2bits(~ i)) +1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 7:
0 ≤ bits2uint(sgn(bitsinvert(uint2bits(~ i)) +1)), i < 0 ⊦ uint2bits(bits2uint(sgn(bitsinvert(uint2bits(~ i)) +1))) = sgn(false ' + sgn(bitsinvert(uint2bits(~ i)) +1))

Rule argument

name: int2bits-pos rotate: F subst: [i] → [bits2uint(sgn(bitsinvert(uint2bits(~ i)) +1))]

Additional information

Used simplifier rules: bits2uint-not-neg-01: ⊦ ¬ bits2uint(bits) < 0;% ⊦ ¬ i ≤ j ↔ j < i; Used terms: bits2uint(sgn(bitsinvert(uint2bits(~ i)) +1))