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Proof step 2 from proof fill-refill (previous step)

# bits ≤ n ⊦ fillsgn(n + 1, false ' + fillsgn(n, bits)).rest = fillsgn(n, bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ n ≤ # bits → fillsgn(n, bits) = bits

Rule argument

name: fillsgn-longer rotate: F subst: [bits, n] → [false ' + fillsgn(n, bits), n + 1]

Additional information

Used simplifier rules: fill-length: ⊦ # bits ≤ n → # fillsgn(n, bits) = n;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: false ' + fillsgn(n, bits), n + 1