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Proof step 4 from proof eqdef (previous step)

ordered≤(y), ordered≤(a + x0), perm(a + x0, y), ∀ y. ordered≤(x0) ∧ ordered≤(y) ∧ perm(x0, y) → x0 = y ⊦ a + x0 = y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
ordered≤(a ' + x0), ordered≤(y), perm(a ' + x0, y), ∀ y0. ordered≤(y0) ∧ perm(x0, y0) → x0 = y0 ⊦ a ' + x0 = y

Rule argument

Additional information

Used simplifier rules: app-01: ⊦ ordered≤(x + y) → ordered≤(y);%cons-02: ⊦ ordered≤(a ' + x) → ordered≤(x);%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)