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Proof step 3 from proof superset-elem-in (previous step)

b ∈ st, st ⊆ st0 ⊦ b ∈ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ st1 ⊆ st2 ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ st1[a] = st2[a])
Proof step 5:
b ∈ st, ∀ a. a ∈ st → a ∈ st0 ∧ st[a] = st0[a] ⊦ b ∈ st0

Rule argument

spec: <toplevel> name: Subset seq: ⊦ st1 ⊆ st2 ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ st1[a] = st2[a]) subst: [st2, st1] → [st0, st] flags: <all paths>

Additional information

Used terms: st0, st