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Proof step 25 from proof and-com (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 27:
1 < # bits0 ∧ 1 < # bits, ∀ bits1, bits. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bitsand(bits, bits1) = bitsand(bits1, bits) ⊦ bits0 = [], bits = [], bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)' = bitsand(bits0.butlast, bits.butlast) + (bits0.last ∧ bits.last), bits = bits.first ', bits0 = bits0.first '

Rule argument

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

Additional information

Used simplifier rules: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ # bits = 0 ↔ bits = [];% ⊦ # bits = 1 ↔ bits = bits.first + [];% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits, bits0