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Proof step 25 from proof bitsand-cast-05 (previous step)

# bits1 = n + 1 + # bits0, # bits0 < # bits1, 1 + # bits0 < # bits1 ⊦ sgn(bitsand(mklist(false, n) + false ' + bits0, false ' + bits1)) = sgn(bitsand(false ' + bits0, false ' + bits1)), bits1 = [], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ¬ true ∈ bits ∧ bits1 ≠ [] → sgn(bitsand(bits + false ' + bits0, bits1)) = sgn(bitsand(false ' + bits0, bits1))

Rule argument

name: bitsand-app-zeros-01 rotate: F subst: [bits1, bits0, bits] → [false ' + bits1, bits0, mklist(false, n)]

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ true ∈ mklist(false, n);% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: false ' + bits1, bits0, mklist(false, n)