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Proof step 73 from proof bxor-flip-one-bit (previous step)

int2bits(i) = boolvar0 ' + boolvar ', 0 < i, 2 < i ⊦ i = 0, (sgn(boolvar0 ' + (¬ boolvar)')[1] ↔ ¬ boolvar) ∧ sgn(boolvar0 ' + (¬ boolvar)')[1, boolvar] = int2bits(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ 1 < i → int2bits(i) = int2bits(i / 2) + (i % 2 = 1)'
Proof step 75:
1 < i, int2bits(i / 2) + (i % 2 = 1)' = boolvar0 ' + boolvar ', 0 < i, 2 < i ⊦ i = 0, (sgn(boolvar0 ' + (¬ boolvar)')[1] ↔ ¬ boolvar) ∧ sgn(boolvar0 ' + (¬ boolvar)')[1, boolvar] = int2bits(i / 2) + (i % 2 = 1)'

Rule argument

seq: ⊦ 1 < i → int2bits(i) = int2bits(i / 2) + (i % 2 = 1)' subst: [i] → [i] rotate: F spec: int2bits inst: name: int2bits-rec-pos-01

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; Used terms: i