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Proof step 6 from proof del-append (previous step)

∀ y, a. (x0 + y) -l a = (x0 -l a) + (y -l a) ⊦ a = a0, ((a0 ' + x0) + y) -l a = ((a0 ' + x0) -l a) + (y -l a)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ y, a. (x0 + y) -l a = (x0 -l a) + (y -l a) ⊦ a = a0, (x0 + y) -l a = (x0 -l a) + (y -l a)

Rule argument

Additional information

Used simplifier rules: del-n: ⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a);%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list