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Proof step 11 from proof cast-law-shift-snd-l (previous step)

# int2bits(31) = m + 1, 5 ≤ i, 0 < i, 0 ≤ i, i < n→i(m), 5 < m ⊦ m = 1, bits2int(int2bits(j0) + mklist(false, i→n(band(j, 31)))) = bits2int(int2bits(j0) + mklist(false, i→n(band(cast(i, j), 31))))

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 + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%n0 < n ⊦ (* n) = m0 + (* n0) ↔ n - n0 = m0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward) Used terms: 31