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Proof step 14 from proof intshiftrzero-prop-01 (previous step)

int2bits(31) = false ' + bits, false ∈ bits, i < 0, ~2147483648 ≤ i, false ∈ int2bits(31) ⊦ bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = bits2int(int2bits(2) + mklist(false, i→n(band(~(j + 1), 31)))) + (i i>> j), band(j, 31) = 0

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

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