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Proof step 4 from proof sgn-mklist-03 (previous step)

∀ boolvar. sgn(mklist(boolvar, m)) = boolvar ' ⊦ sgn(boolvar ' + mklist(boolvar, m)) = boolvar ', m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
Proof step 6:
¬(mklist(boolvar, m) ≠ [] ∧ (mklist(boolvar, m).first ↔ boolvar)), ∀ boolvar. sgn(mklist(boolvar, m)) = boolvar ' ⊦ sgn(boolvar ' + mklist(boolvar, m)) = boolvar ', m = 0
Proof step 8:
mklist(boolvar, m) ≠ [] ∧ (mklist(boolvar, m).first ↔ boolvar), ∀ boolvar. sgn(mklist(boolvar, m)) = boolvar ' ⊦ sgn(mklist(boolvar, m)) = boolvar ', m = 0

Rule argument

name: sgn-rec-01 rotate: F subst: [bits, boolvar] → [mklist(boolvar, m), boolvar]

Additional information

Used terms: mklist(boolvar, m), boolvar