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Proof step 14 from proof bitsand-cast-04 (previous step)

# bits1 ≤ # bits0 + n0 ⊦ n0 = 0, sgn(bitsand(lastn((1 + # bits0) + n0, mklist(boolvar, n0) + boolvar ' + bits0), false ' + bits1)) = sgn(bitsand(boolvar ' + bits0, false ' + bits1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 16:
(1 + # bits0) + n0 = #(mklist(boolvar, n0) + boolvar ' + bits0), # bits1 ≤ # bits0 + n0 ⊦ n0 = 0, sgn(bitsand(mklist(boolvar, n0) + boolvar ' + bits0, false ' + bits1)) = sgn(bitsand(boolvar ' + bits0, false ' + bits1))

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [mklist(boolvar, n0) + boolvar ' + bits0, (1 + # bits0) + n0] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (m + n0) + n1 = m + n0 + n1; Used terms: mklist(boolvar, n0) + boolvar ' + bits0, (1 + # bits0) + n0