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Proof step 3 from proof size-del-02 (previous step)

a ∈ st, # st.keys ≤ # (st -- a).keys ⊦ a < st.min

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ a ∈ st.keys → (st -- a).keys = st.keys -- a
Proof step 5:
a ∈ st, a ∈ st.keys, # st.keys ≤ #(st.keys -- a) ⊦ a < st.min

Rule argument

spec: <toplevel> name: del-01 seq: ⊦ a ∈ st.keys → (st -- a).keys = st.keys -- a subst: [a, st] → [a, st] flags: <all paths>

Additional information

Used simplifier rules: Keys: ⊦ a ∈ st.keys ↔ a ∈ st; Used terms: a, st