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Proof step 4 from proof bitsand-cast-05 (previous step)

# bits1 ≤ n ⊦ bits = [], n = 0, sgn(bitsand(lastn(n, fillsgn(n, bits)), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ # bits0 ≤ n ∧ ¬ bits0.first ∧ bits ≠ [] ∧ bits0 ≠ [] → sgn(bitsand(lastn(n, fillsgn(n, bits)), bits0)) = sgn(bitsand(bits, bits0))
Proof step 6:
¬(#(false ' + bits1) ≤ n ∧ ¬ (false ' + bits1).first ∧ bits ≠ [] ∧ false ' + bits1 ≠ []), # bits1 ≤ n ⊦ bits = [], n = 0, sgn(bitsand(lastn(n, fillsgn(n, bits)), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1))

Rule argument

name: bitsand-cast-04 rotate: F subst: [bits0, bits, n] → [false ' + bits1, bits, n]

Additional information

Used terms: false ' + bits1, bits, n