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Proof step 16 from proof bitsand-app (previous step)

# bits1 = # bits4, ∀ bits2, bits0, bits, bits3. # bits3 < #(bits4 + boolvar ') → # bits = # bits3 → bits0 = [] ∨ bits2 = [] ∨ bits = [] ∨ bitsand(bits0 + bits, bits2 + bits3) = bitsand(bits0, bits2) + bitsand(bits, bits3) ⊦ bits2 = [], bits0 = [], bitsand(bits0 + bits1, bits2 + bits4) = bitsand(bits0, bits2) + bitsand(bits1, bits4), bits1 = [], bits4 = []

User applied rule apply induction

And closed the goal!

Rule argument

subst: [bits2, bits0, bits, bits3] → [bits2, bits0, bits1, bits4]

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ ¬ n < n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bits2, bits0, bits1, bits4