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Proof step 12 from proof del (previous step)

#oc(a, y) + 1 < #oc(a, x), a ∈ x, x -1l a ⊆m y, y ⊆m x -1l a ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y))
Proof step 14:
#oc(a, y) + 1 < #oc(a, x), a ∈ x, y ⊆m x -1l a, ∀ a0. #oc(a0, x -1l a) ≤ #oc(a0, y) ⊦

Rule argument

spec: <toplevel> name: msubset seq: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y)) subst: [y, x] → [y, x -1l a] flags: <all paths>

Additional information

Used terms: y, x -1l a