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Proof step 15 from proof butmin-rewput (previous step)

⊦ a0 = a, a = st[a, d].min, a0 = st[a, d].min, (a0 ∈ st ↔ a0 ∈ st -- st.min) ∧ st[a0] = (st -- st.min)[a0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ a ≠ b → (st -- b)[a] = st[a]
Proof step 17:
¬ a0 ≠ st.min ⊦ a0 = a, a = st[a, d].min, a0 = st[a, d].min, (a0 ∈ st ↔ a0 ∈ st -- st.min) ∧ st[a0] = (st -- st.min)[a0]

Rule argument

spec: store inst: name: Del-at seq: ⊦ a ≠ b → (st -- b)[a] = st[a] subst: [a, b, st] → [a0, st.min, st] flags: rewrite

Additional information

Used simplifier rules: Del-in: ⊦ a ∈ st -- b ↔ a ≠ b ∧ a ∈ st; from specification store Used terms: a0, st.min, st