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Proof step 9 from proof bitsand-first-samesize (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 11:
¬(1 < # bits1 ∧ 1 < # bits), # bits1 = # bits, ∀ boolvar0, boolvar, bits1, bits0. # bits0 < # bits → # bits1 = # bits0 → bits0 = [] ∨ bitsand(boolvar ' + bits1, boolvar0 ' + bits0) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits0) ⊦ bitsand(boolvar ' + bits1, boolvar0 ' + bits) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits), bits = []
Proof step 24:
1 < # bits1 ∧ 1 < # bits, # bits1 = # bits, ∀ boolvar0, boolvar, bits1, bits0. # bits0 < # bits → # bits1 = # bits0 → bits0 = [] ∨ bitsand(boolvar ' + bits1, boolvar0 ' + bits0) = (boolvar ∧ boolvar0)' + bitsand(bits1, bits0) ⊦ bitsand(boolvar ' + bits1, boolvar0 ' + bits) = (boolvar ∧ boolvar0)' + (bitsand(bits1.butlast, bits.butlast) + (bits1.last ∧ bits.last)), bits = []

Rule argument

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

Additional information

Used terms: bits, bits1