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Proof step 4 from proof subdel-01 (previous step)

x ⊆m y + (y0 -1l a), a ∈ y0 ⊦ ∀ a0. #oc(a0, x) ≤ #oc(a0, (y + y0) -1l a)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
#oc(a0, (y + y0) -1l a) < #oc(a0, x), a ∈ y0, x ⊆m y + (y0 -1l a), a0 ∈ x ⊦

Rule argument

Additional information

Used simplifier rules: oc-zero: ⊦ #oc(a, x) = 0 ↔ ¬ a ∈ x;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat