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Proof step 8 from proof diff-wfrec (previous step)

¬ a ≠ a0, ∀ a, y. x0 \ (a ' + y) = (x0 -l a) \ y, a0 = a ∨ a0 ∈ y ⊦ x0 \ (a ' + y) = ((a0 ' + x0) -l a) \ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ a, y. x0 \ (a ' + y) = (x0 -l a) \ y ⊦ x0 \ (a0 ' + y) = (x0 -l a0) \ y

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%del-y: ⊦ (a ' + x) -l a = x -l a; from specification list-del