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Proof step 43 from proof lastn-fill-sgn (previous step)

1 + # bits = # fillsgn(1 + # bits, sgn(false ' + bits)), # sgn(false ' + bits) ≤ # bits, # sgn(false ' + bits) < # bits + # bits1 ⊦ fillsgn(1 + # bits, sgn(false ' + bits)) = false ' + bits, bits1 = [], true ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ n = # bits ∧ bits ≠ [] → fillsgn(n, sgn(bits)) = bits

Rule argument

name: fill-sgn-04 rotate: F subst: [bits, n] → [false ' + bits, 1 + # bits]

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ []; Used terms: false ' + bits, 1 + # bits