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Proof step 49 from proof bitsand-app-zeros-01 (previous step)

false ∈ bitsand(bits + false ' + bits3, bits4), false ∈ bitsand(false ' + bits3, bits4), true ∈ bitsand(false ' + bits3, bits4), ∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ bits4 = [], sgn(bitsand(bits + false ' + bits3, bits4)) = sgn(bitsand(false ' + bits3, bits4)), true ∈ bits

User applied rule apply induction

And closed the goal!

Rule argument

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