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Proof step 84 from proof bitsand-cast-01 (previous step)

# bits1 = # bitsand(bits1, true ' + bits), # bits < # bits1 ⊦ bits1 = [], bits2 = [], bits2 + bits1 = [], bitsand(bits1, true ' + bits) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, true ' + bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
⊦ n ≤ # bits → fillsgn(n, bits) = bits

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [bits2 + bitsand(bits1, true ' + bits), # bits1] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used simplifier rules: ⊦ n = # bits → lastn(n, bits0 + bits) = bits;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bits2 + bitsand(bits1, true ' + bits), # bits1