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Proof step 4 from proof bitsand-app-zeros-01 (previous step)

∀ bits0, bits, bits2. # bits2 < # bits1 → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits0, bits1)) = sgn(bitsand(false ' + bits0, bits1)), bits1 = [], true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 6:
¬(1 < #(false ' + bits0) ∧ 1 < # bits1), ∀ bits0, bits, bits2. # bits2 < # bits1 → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits0, bits1)) = sgn(bitsand(false ' + bits0, bits1)), bits1 = [], true ∈ bits
Proof step 21:
1 < #(false ' + bits0) ∧ 1 < # bits1, ∀ bits0, bits, bits2. # bits2 < # bits1 → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits0, bits1)) = sgn(bitsand((false ' + bits0).butlast, bits1.butlast) + ((false ' + bits0).last ∧ bits1.last)), bits1 = [], true ∈ bits

Rule argument

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

Additional information

Used terms: bits1, false ' + bits0