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Proof step 9 from proof sw-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
∀ a, b. (x0 -1l a) -1l b = (x0 -1l b) -1l a ⊦ a0 = a, (a0 ' + (x0 -1l a)) -1l b = ((a0 ' + x0) -1l b) -1l a

Rule argument

Additional information

Used simplifier rules: del1-n: ⊦ a ≠ b → (b ' + x) -1l a = b ' + (x -1l a);%a: ⊦ (x + y) + z = x + y + z; from specification list