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Proof step 18 from proof fill-last (previous step)

m0 < # bits, ∀ bits, boolvar. bits = [] ∨ fillsgn(m0 + 1, bits + boolvar ') = fillsgn(m0, bits) + boolvar ' ⊦ bits = [], bits = fillsgn(m0 + 1, bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ n ≤ # bits → fillsgn(n, bits) = bits

Rule argument

name: fillsgn-longer rotate: F subst: [bits, n] → [bits, m0 + 1]

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ ¬ n < n; Used terms: bits, m0 + 1