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Proof step 506 from proof bitsand-cast (previous step)

# bits1 = # bitsand(bits1, true ' + false ' + bits), # bits1 = 2 + # bits ⊦ bits4 + bits1 = [], bits1 = [], lastn(# bits1, fillsgn(# bits1, bits4 + bitsand(bits1, true ' + false ' + bits))) = bitsand(bits1, true ' + false ' + bits), bits2 = [], bits4 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 507:
⊦ n ≤ # bits → fillsgn(n, bits) = bits

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [bits4 + bitsand(bits1, true ' + false ' + 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 → n ≠ 0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ m + n < m; Used terms: bits4 + bitsand(bits1, true ' + false ' + bits), # bits1