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Proof step 7 from proof band-31-pos (previous step)

int2bits(31) = false ' + bits, false ∈ bits, 0 ≤ i, i < 32, false ∈ int2bits(31) ⊦ band(i, 31) = i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i ⊦ int2bits((* i)) = uint2bits(i) subst: [i] → [31] rotate: F spec: int2bits inst: name: int2bits-pos-num

Additional information

Used simplifier rules: 1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);% ⊦ uint2bits(1) = false + true;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bits + boolvar = bits + boolvar ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ bits + boolvar ' = bits0 → boolvar ∈ bits0; (forward) Used terms: 31