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Proof step 36 from proof and-insgn (previous step)

∀ bits1, bits, boolvar. # bits1 < #(bits2 + boolvar0 ') → true → bits = [] ∨ bits1 = [] ∨ (boolvar ∈ bitsand(sgn(bits), bits1) ↔ boolvar ∈ bitsand(bits, bits1)) ⊦ bits2 + boolvar0 ' = (bits2 + boolvar0 ').first ', bits0 + boolvar1 ' = (bits0 + boolvar1 ').first ', boolvar ∈ bitsand(sgn(bits0 + boolvar1 '), bits2 + boolvar0 ') ↔ (boolvar ↔ boolvar1 ∧ boolvar0) ∨ boolvar ∈ bitsand(bits0, bits2), (¬ boolvar1) ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
¬ (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = boolvar '
Proof step 38:
¬ (¬ boolvar1) ∈ bits0, ∀ bits1, bits, boolvar. # bits1 < #(bits2 + boolvar0 ') → true → bits = [] ∨ bits1 = [] ∨ (boolvar ∈ bitsand(sgn(bits), bits1) ↔ boolvar ∈ bitsand(bits, bits1)) ⊦ bits2 + boolvar0 ' = (bits2 + boolvar0 ').first ', bits0 + boolvar1 ' = (bits0 + boolvar1 ').first ', boolvar ∈ bitsand(boolvar1 ', bits2 + boolvar0 ') ↔ (boolvar ↔ boolvar1 ∧ boolvar0) ∨ boolvar ∈ bitsand(bits0, bits2), (¬ boolvar1) ∈ bits0

Rule argument

seq: ¬ (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = boolvar ' subst: [boolvar, bits] → [boolvar1, bits0] rotate: F spec: bitopsaux inst: name: sgn-last-same

Additional information

Used terms: boolvar1, bits0