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

# bits3 + 1 < # bits0, ∀ bits, bits0, bits1. # bits1 < #(bits3 + boolvar ') → # bits1 < # bits0 → bitsand(bits + bits0, true ' + bits1) = bits + bitsand(bits0, true ' + bits1) ∨ bits0 = [] ⊦ # bits + # bits0 = 0, bits0 = [], bitsand(bits + bits0.butlast, true ' + bits3) + (bits0.last ∧ boolvar)' = bits + bitsand(bits0, true ' + bits3 + boolvar '), # bits0 = 1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
bits0 = bits2 + boolvar0 ', # bits3 + 1 < # bits0, ∀ bits, bits0, bits1. # bits1 < #(bits3 + boolvar ') → # bits1 < # bits0 → bitsand(bits + bits0, true ' + bits1) = bits + bitsand(bits0, true ' + bits1) ∨ bits0 = [] ⊦ # bits + # bits0 = 0, bits0 = [], bitsand(bits + bits2, true ' + bits3) + (boolvar0 ∧ boolvar)' = bits + bitsand(bits0, true ' + bits3 + boolvar '), # bits0 = 1

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits0, boolvar0, bits2] 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, boolvar0, bits2