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Proof step 34 from proof bitsand-cast (previous step)

n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n0 + 1 + # bits1 < n, bits0.first, # bits0 ≤ 2 + # bits1, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n ⊦ n = # fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), boolvar ↔ boolvar0, n0 = 0, lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0))) = lastn(n, fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0))), bits0 = [], boolvar ∧ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ # bits ≤ n → # fillsgn(n, bits) = n

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n