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Proof step 12 from proof bitsand-first-samesize (previous step)

# bits1 = 1, # bits = 1, ∀ boolvar0, boolvar, bits1, bits0. # bits0 < 1 → # bits1 = # bits0 → bits0 = [] ∨ bitsand(boolvar ' + bits1, boolvar0 ' + bits0) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits0) ⊦ bits1 = [], bits = [], bitsand(boolvar ' + bits1, boolvar0 ' + bits) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ bits ≠ [] ∧ bits0 = true ' → bitsand(bits, bits0) = bits
Proof step 14:
¬(bits1 ≠ [] ∧ bits = true '), # bits1 = 1, # bits = 1, ∀ boolvar0, boolvar, bits1, bits0. # bits0 < 1 → # bits1 = # bits0 → bits0 = [] ∨ bitsand(boolvar ' + bits1, boolvar0 ' + bits0) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits0) ⊦ bits1 = [], bits = [], bitsand(boolvar ' + bits1, boolvar0 ' + bits) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits)
Proof step 19:
bits1 ≠ [] ∧ bits = true ', # bits1 = 1, # bits = 1, ∀ boolvar0, boolvar, bits1, bits0. # bits0 < 1 → # bits1 = # bits0 → bits0 = [] ∨ bitsand(boolvar ' + bits1, boolvar0 ' + bits0) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits0) ⊦ bits1 = [], bits = [], bitsand(boolvar ' + bits1, boolvar0 ' + bits) = (boolvar ∧ boolvar0)' + bits1

Rule argument

name: and-rec-01 rotate: F subst: [bits0, bits] → [bits, bits1]

Additional information

Used terms: bits, bits1