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Proof step 22 from proof bitsand-app-zeros-01 (previous step)

∀ bits0, bits, bits2. # bits2 < # bits1 → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ bits0 = [], bits1 = [], sgn(bitsand(bits + false ' + bits0, bits1)) = sgn(bitsand(false ' + bits0.butlast, bits1.butlast) + (bits0.last ∧ bits1.last)'), # bits1 = 1, true ∈ bits

User applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
bits0 = bits3 + boolvar ', ∀ bits0, bits, bits2. # bits2 < # bits1 → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ bits0 = [], bits1 = [], sgn(bitsand(bits + false ' + bits0, bits1)) = sgn(bitsand(false ' + bits3, bits1.butlast) + (boolvar ∧ bits1.last)'), # bits1 = 1, true ∈ bits

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits0, boolvar, bits3] rotate: T spec: list-last inst: bitlista name: last-elim

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar '; (elim) Used terms: bits0, boolvar, bits3