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Proof step 2 from proof butmin-put-rew (previous step)

st.keys.min < a, st.keys.min ∈ st ⊦ st = ∅, (st -- st.keys.min)[a, d] = st[a, d] -- st.keys.min

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ a ≠ b → (st -- b)[a, d] = st[a, d] -- b

Rule argument

spec: store inst: name: delete-put-rew seq: ⊦ a ≠ b → (st -- b)[a, d] = st[a, d] -- b subst: [d, a, b, st] → [d, a, st.keys.min, st] flags: rewrite

Additional information

Used simplifier rules: del-put: ⊦ (st -- a)[a, d] = st[a, d]; from specification store%insert: ⊦ st[a, d] -- a = st -- a; from specification store%irreflexivity: ⊦ ¬ a < a; from specification oelem Used terms: d, a, st.keys.min, st