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Proof step 12 from proof fill-sgn-02 (previous step)

fillsgn(1 + # bits, sgn(boolvar0 ' + bits)) = boolvar0 ' + bits, boolvar0 → ¬ boolvar ⊦ boolvar0 ↔ boolvar, fillsgn(2 + # bits, boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ n ≤ # bits → fillsgn(n, bits) = bits

Rule argument

name: fillsgn-longer rotate: F subst: [bits, n] → [boolvar ' + boolvar0 ' + bits, 2 + # bits]

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ n < n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: boolvar ' + boolvar0 ' + bits, 2 + # bits