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Proof step 9 from proof fill-sgn-01 (previous step)

n1 + # bits0 < # sgn(boolvar ' + bits0), ∀ n0. ¬ n0 < # bits0 → fillsgn(n0, sgn(bits0)) = fillsgn(n0, bits0) ⊦ n1 = 0, fillsgn(n1 + # bits0, sgn(boolvar ' + bits0)) = mklist(boolvar, n1) + bits0

User applied rule insert lemma

And obtained the following new goals

Rule argument

name: sgn-length subst: [bits] → [boolvar ' + bits0]

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m < 1 ↔ m = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: boolvar ' + bits0