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Proof step 54 from proof bitsand-fillsgn (previous step)

¬(# mklist(true, # bits2) = # bits2 ∧ mklist(true, n0) ≠ [] ∧ false ' ≠ [] ∧ mklist(true, # bits2) ≠ []), ∀ n, bits, bits1. # bits1 < #(false + bits2) → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ fillsgn(n0 + # bits2, bitsand(mklist(true, n0) + mklist(true, # bits2), false ' + bits2)) = mklist(false, n0) + bits2, n0 = 0, n0 = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
∀ n, bits, bits1. # bits1 < #(false + []) → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ n0 = 1, n0 = 0, fillsgn(n0, bitsand(mklist(true, n0), false ')) = mklist(false, n0)

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;% ⊦ # [] = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ boolvar ' ≠ [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ # mklist(boolvar, n) = n;