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Proof step 12 from proof and-size-one-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 14:
¬(1 < #(bits3 + boolvar ') ∧ 1 < #(bits2 + boolvar0 ')), # bits3 = # bits2, ∀ bits, bits1, bits0. # bits < #(bits3 + boolvar ') → # bits = # bits1 → bits1 = [] ∨ bits0 = [] ∨ bitsand(true ' + bits, bits0 + bits1) = bits0 + bitsand(bits, bits1) ⊦ bits0 = [], bitsand(true ' + bits3, bits0 + bits2) + (boolvar ∧ boolvar0)' = bits0 + bitsand(bits3 + boolvar ', bits2 + boolvar0 ')
Proof step 16:
1 < #(bits3 + boolvar ') ∧ 1 < #(bits2 + boolvar0 '), # bits3 = # bits2, ∀ bits, bits1, bits0. # bits < #(bits3 + boolvar ') → # bits = # bits1 → bits1 = [] ∨ bits0 = [] ∨ bitsand(true ' + bits, bits0 + bits1) = bits0 + bitsand(bits, bits1) ⊦ bits0 = [], bitsand(true ' + bits3, bits0 + bits2) + (boolvar ∧ boolvar0)' = bits0 + (bitsand((bits3 + boolvar ').butlast, (bits2 + boolvar0 ').butlast) + ((bits3 + boolvar ').last ∧ (bits2 + boolvar0 ').last))

Rule argument

name: and-rec rotate: F subst: [bits0, bits] → [bits2 + boolvar0 ', bits3 + boolvar ']

Additional information

Used terms: bits2 + boolvar0 ', bits3 + boolvar '