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Proof step 8 from proof subset-emp (previous step)

bag ⊆ ∅ ⊦ count(a, bag) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ bag0 ⊆ bag1 ↔ (∀ a. count(a, bag0) ≤ count(a, bag1))
Proof step 10:
∀ a. count(a, bag) ≤ count(a, ∅) ⊦ count(a, bag) = 0

Rule argument

spec: <toplevel> name: count-subset seq: ⊦ bag0 ⊆ bag1 ↔ (∀ a. count(a, bag0) ≤ count(a, bag1)) subst: [bag1, bag0] → [∅, bag] flags: <all paths>

Additional information

Used terms: ∅, bag