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Proof step 17 from proof and-011x-neg (previous step)

bitsand(false ' + bits0.butlast, true ' + bits2.butlast) + (bits0.last ∧ bits2.last)' = false ' + bits1, ∀ bits, bits2, bits1. # bits < # bits0 → bitsand(false ' + bits, true ' + bits2) = false ' + bits1 → 2 ^ n→i(# bits) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits) + bits2uint(bits1) ∨ false ∈ bits ⊦ bits2 = [], bits0 = [], 2 ^ n→i(# bits0) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits0) + bits2uint(bits1), false ∈ bits0, ¬ (bits0.last ∧ bits2.last) ∈ bits1 ∧ bits0.last ∧ bits2.last, (bits0.last ∧ bits2.last) ∧ ¬ false ∈ bitsand(false ' + bits0.butlast, true ' + bits2.butlast)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
bits0 = bits3 + boolvar ', bitsand(false ' + bits3, true ' + bits2.butlast) + (boolvar ∧ bits2.last)' = false ' + bits1, ∀ bits, bits2, bits1. # bits < # bits0 → bitsand(false ' + bits, true ' + bits2) = false ' + bits1 → 2 ^ n→i(# bits) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits) + bits2uint(bits1) ∨ false ∈ bits ⊦ bits2 = [], bits0 = [], 2 ^ n→i(# bits0) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits0) + bits2uint(bits1), false ∈ bits0, ¬ (boolvar ∧ bits2.last) ∈ bits1 ∧ boolvar ∧ bits2.last, (boolvar ∧ bits2.last) ∧ ¬ false ∈ bitsand(false ' + bits3, true ' + bits2.butlast)

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