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Proof step 402 from proof bitsand-cast (previous step)

¬(# bits1 = #(true ' + false ' + bits) ∧ bits3 ≠ [] ∧ bits2 + mklist(true, n - 1) ≠ [] ∧ bits1 ≠ []), # bits1 = 2 + # bits, sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3 + bits1, (bits2 + mklist(true, n - 1)) + true ' + false ' + bits))), n = 0, bits3 + bits1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 403:
n - 1 = 0, # bits1 = 2 + # bits ⊦ bits3 = [], bits1 = [], bits3 + bits1 = [], n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3 + bits1, true ' + false ' + bits)))

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ sgn(true ' + false ' + bits) = true ' + false ' + bits;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0;% ⊦ # [] = 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;