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Proof step 3 from proof eqdef (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
ordered≤(a ' + x0), perm(a ' + x0, y), ordered≤(y), ∀ y0. perm(x0, y0) ∧ ordered≤(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%c: ⊦ a + x = a ' + x; from specification list