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Proof step 3 from proof del-del1-nodups (previous step)

∀ a. x0 -l a = x0 -1l a ∨ dups(x0) ⊦ (a0 + x0) -l a = (a0 + x0) -1l a, dups(a0 + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ a1. x0 -l a1 = x0 -1l a1 ⊦ (a0 ' + x0) -l a = (a0 ' + x0) -1l a, a0 ∈ x0, dups(x0)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%rec: ⊦ dups(a ' + x) ↔ ¬ ¬(a ∈ x ∨ dups(x)); from specification list-dup%c: ⊦ a + x = a ' + x; from specification list