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Proof step 59 from proof shiftright-rec-pos (previous step)

0 ≤ i0, true ∈ firstn(1, mklist(false, i→n(i0)) + false ' + false ') ⊦ bits2int(firstn(1, mklist(false, i→n(i0)) + false ' + false ')) = 0, true ∈ firstn(1, mklist(false, i→n(i0)) + false ')

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ ¬ boolvar ∈ bits ∧ n ≤ # bits → ¬ boolvar ∈ firstn(n, bits) subst: [bits, n, boolvar] → [mklist(false, i→n(i0)) + false ' + false ', 1, true] rotate: F spec: list-del inst: bitlista name: firstN-in

Additional information

Used simplifier rules: ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ ¬ true ∈ mklist(false, n);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;%n < n0 ⊦ (* n) ≤ m0 + (* n0);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(false, i→n(i0)) + false ' + false ', 1, true