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Proof step 85 from proof byte-law-righthift-not (previous step)

31 = n + # int2bits(~128), 32 = n + # int2bits(128), i2b(bits2uint(firstn(31, mklist(false, n) + int2bits(128)))) = i2b(bits2uint(firstn(31, (mklist(true, n) + true ') + int2bits(~128)))), # int2bits(128) ≤ 32, # int2bits(~128) ≤ 32 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m ≤ # bits + # bits0 ∧ # bits ≤ m → firstn(m, bits + bits0) = bits + firstn(m - # bits, bits0) subst: [bits0, bits, m] → [int2bits(128), mklist(false, n), 31] rotate: F spec: list-del inst: bitlista name: firstn-app-02

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n → n ≠ 0;% ⊦ ¬ m + n < m; Used terms: int2bits(128), mklist(false, n), 31