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Proof step 3 from proof size-del (previous step)

st.keys = ∅, a ∈ st, 0 ≤ 0 - 1 ⊦ a < st.min

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ a ∈ st ↔ a ∈ st.keys

Rule argument

spec: <toplevel> name: inkeys seq: ⊦ a ∈ st ↔ a ∈ st.keys subst: [st, a] → [st, a] flags: <all paths>

Additional information

Used simplifier rules: notempty: ⊦ a ∈ st.keys → st.keys ≠ ∅; Used terms: st, a