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Proof step 176 from proof byte-law-and-one (previous step)

# int2bits(i) ≤ 8 ∧ int2bits(i) ≠ [], 7 = # fillsgn(7, int2bits(i)), # bits1 = # int2bits(i), int2bits(j) = (bits0 + bits2) + bits1, # bits2 + # bits1 = 8, # bits1 < 8, # bits1 < # bits0 + # bitsand(bits2 + bits1, mklist(int2bits(i).first, 8 - # int2bits(i)) + int2bits(i)), # bits1 < # bitsand(bits2 + bits1, mklist(int2bits(i).first, 8 - # int2bits(i)) + int2bits(i)), i < 0, 8 ≤ # bits0 + # bitsand(bits2 + bits1, mklist(int2bits(i).first, 8 - # int2bits(i)) + int2bits(i)), 8 ≤ # bitsand(bits2 + bits1, mklist(int2bits(i).first, 8 - # int2bits(i)) + int2bits(i)), 8 ≤ # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), # bits1 < # bits0 + # bits2 + # bitsand(bits1, int2bits(i)) ⊦ bits2 = [], bitsand(bits2 + bits1, mklist(int2bits(i).first, 8 - # int2bits(i)) + int2bits(i)) = [], lastn(8, (bits0 + bits2) + bitsand(bits1, int2bits(i))) = lastn(8, bitsand(bits2 + bits1, mklist(int2bits(i).first, 8 - # int2bits(i)) + int2bits(i)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 177:
# bits2 + # bits1 = 8, int2bits(j) = (bits0 + bits2) + bits1, # bits1 = # int2bits(i), 7 = # fillsgn(7, int2bits(i)), # bits1 < # bitsand(bits2 + bits1, mklist(true, 8 - # bits1) + int2bits(i)), # bits1 < # bitsand(bits2 + bits1, mklist(true, 8 - # bits1) + int2bits(i)) + # bits0, 8 ≤ # bitsand(bits2 + bits1, mklist(true, 8 - # bits1) + int2bits(i)), 8 ≤ # bitsand(bits2 + bits1, mklist(true, 8 - # bits1) + int2bits(i)) + # bits0, i < 0, # bits1 < 8, # bits1 < # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), 8 ≤ # bits0 + # bits2 + # bitsand(bits1, int2bits(i)) ⊦ lastn(8, (bits0 + bits2) + bitsand(bits1, int2bits(i))) = lastn(8, bitsand(bits2 + bits1, mklist(true, 8 - # bits1) + int2bits(i))), bitsand(bits2 + bits1, mklist(true, 8 - # bits1) + int2bits(i)) = [], bits2 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n;% ⊦ m < n → n ≠ 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)%0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ int2bits(j) ≠ [];% ⊦ j < 0 → int2bits(j).first;