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Proof step 8 from proof del1-del-switch (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ a, b. (x0 -l a) -1l b = (x0 -1l b) -l a ∨ a = b ⊦ (a0 ' + (x0 -l a)) -1l b = ((a0 ' + x0) -1l b) -l a, a = a0, a = b

Rule argument

Additional information

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