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Proof step 76 from proof fix-bits2bytes (previous step)

# bits = m * 8 + n0, n0 < 8, # bits2bytes(bits) < n, # bits ≤ 8 * (n - 1), m < n ⊦ bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, n * 8 - # bits) + bits), n * 8 = # bits, n0 = 0, n * 8 = m * 8 + 8 + (n - 1 - m) * 8, bits.first

User applied rule insert elim lemma

And closed the goal!

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m0] rotate: T spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: ⊦ ¬ n < 0;%n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ # bits = 0 ↔ bits = [];% ⊦ m + n = n + m;% ⊦ m * (n + 1) = m * n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ m * n + m0 * n = m1 * n ↔ ¬ ¬(m + m0 = m1 ∨ n = 0);% ⊦ m < n → (n ≤ m ↔ false);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ mklist(by, n) + by ' = by ' + mklist(by, n);% ⊦ mklist(by, 1) = by ';% ⊦ mklist(by, m + n) = mklist(by, m) + mklist(by, n);% ⊦ m + 1 ≠ 0;% ⊦ ¬ m ≤ n ↔ n < m;%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m0