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Proof step 92 from proof bitsor-bi-sgn (previous step)

bits2int(bitsor(sgn(boolvar1 ' + bits0), bits3)) = ~1, (¬ boolvar1) ∈ bits0, bitsor(boolvar1 ' + bits0, bits3).first, boolvar ∨ boolvar0, ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bitsor(boolvar1 ' + bits0, bits3) = [], bits3 = [], bits2int(bitsor(sgn(boolvar1 ' + bits0), bits3) + true ') = ~1, false ∈ bitsor(boolvar1 ' + bits0, bits3), ¬ boolvar ∧ ¬ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 93:
⊦ ¬ false ∈ bits ∧ bits ≠ [] → bits2int(bits) = ~1
Proof step 94:
¬(¬ false ∈ bitsor(sgn(boolvar1 ' + bits0), bits3) + true ' ∧ bitsor(sgn(boolvar1 ' + bits0), bits3) + true ' ≠ []), bits2int(bitsor(sgn(boolvar1 ' + bits0), bits3)) = ~1, (¬ boolvar1) ∈ bits0, bitsor(boolvar1 ' + bits0, bits3).first, boolvar ∨ boolvar0, ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bitsor(boolvar1 ' + bits0, bits3) = [], bits3 = [], bits2int(bitsor(sgn(boolvar1 ' + bits0), bits3) + true ') = ~1, false ∈ bitsor(boolvar1 ' + bits0, bits3), ¬ boolvar ∧ ¬ boolvar0

Rule argument

seq: ⊦ ¬ false ∈ bits ∧ bits ≠ [] → bits2int(bits) = ~1 subst: [bits] → [bitsor(sgn(boolvar1 ' + bits0), bits3) + true '] rotate: F spec: int2bits inst: name: bits2int-ones

Additional information

Used terms: bitsor(sgn(boolvar1 ' + bits0), bits3) + true '