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Proof step 36 from proof bitsor-bi-sgn (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ ¬ boolvar ∈ bits → sgn(boolvar ' + bits) = boolvar ' + bits
Proof step 38:
¬ ¬ boolvar1 ∈ boolvar ', ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits3 = [], bits2int(bitsor(sgn(boolvar1 ' + boolvar '), bits3 + boolvar0 ')) = bits2int(bitsor(boolvar1 ' + bits0, bits3) + (boolvar ∨ boolvar0)'), (¬ boolvar1) ∈ bits0
Proof step 53:
¬ boolvar1 ∈ boolvar ', ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits3 = [], bits2int(bitsor(boolvar1 ' + boolvar ', bits3 + boolvar0 ')) = bits2int(bitsor(boolvar1 ' + bits0, bits3) + (boolvar ∨ boolvar0)'), (¬ boolvar1) ∈ bits0

Rule argument

seq: ⊦ ¬ boolvar ∈ bits → sgn(boolvar ' + bits) = boolvar ' + bits subst: [bits, boolvar] → [boolvar ', boolvar1] rotate: F spec: bitopsaux inst: name: sgn-base-04

Additional information

Used terms: boolvar ', boolvar1