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Proof step 57 from proof bitsor-bi-sgn (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
⊦ bits0 ≠ [] ∧ bits = true ' → bitsor(bits, bits0) = true '
Proof step 59:
¬(bits3 ≠ [] ∧ boolvar1 ' = true '), ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ boolvar1 ↔ boolvar, bits3 = [], bits2int(bitsor(boolvar1 ', bits3) + (boolvar ∨ boolvar0)') = bits2int(bitsor(boolvar1 ' + bits0, bits3) + (boolvar ∨ boolvar0)'), (¬ boolvar1) ∈ bits0
Proof step 65:
bits3 ≠ [] ∧ boolvar1 ' = true ', ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ boolvar1 ↔ boolvar, bits3 = [], bits2int(true ' + (boolvar ∨ boolvar0)') = bits2int(bitsor(boolvar1 ' + bits0, bits3) + (boolvar ∨ boolvar0)'), (¬ boolvar1) ∈ bits0

Rule argument

name: or-rec-03 rotate: F subst: [bits0, bits] → [bits3, boolvar1 ']

Additional information

Used terms: bits3, boolvar1 '