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Proof step 21 from proof and-size-one (previous step)

bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = true ', # bits0 + # bits1 = 0, bits1 = [], bits = [], bitsand(bits.butlast, bits0 + bits1.butlast) + (bits1.last ∧ bits.last)' = bits0 + bitsand(bits.butlast, bits1.butlast) + (bits.last ∧ bits1.last)', bits1 = bits1.first '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ bits + boolvar ' = bits0 + boolvar0 ' ↔ bits = bits0 ∧ (boolvar ↔ boolvar0)
Proof step 23:
bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = true ', # bits0 + # bits1 = 0, bits1 = [], bits = [], bitsand(bits.butlast, bits0 + bits1.butlast) = bits0 + bitsand(bits.butlast, bits1.butlast) ∧ (bits1.last ∧ bits.last ↔ bits.last ∧ bits1.last), bits1 = bits1.first '

Rule argument

seq: ⊦ bits + boolvar ' = bits0 + boolvar0 ' ↔ bits = bits0 ∧ (boolvar ↔ boolvar0) subst: [boolvar0, bits0, boolvar, bits] → [bits.last ∧ bits1.last, bits0 + bitsand(bits.butlast, bits1.butlast), bits1.last ∧ bits.last, bitsand(bits.butlast, bits0 + bits1.butlast)] rotate: F spec: list inst: bitlista name: app-06

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits.last ∧ bits1.last, bits0 + bitsand(bits.butlast, bits1.butlast), bits1.last ∧ bits.last, bitsand(bits.butlast, bits0 + bits1.butlast)