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Proof step 4 from proof Diff-get (previous step)

∀ a, st. ¬ a ∈ s0 → (st \ s0)[a] = st[a] ⊦ ¬ a ∈ s0 ++ a0 → ((st \ s0) -- a0)[a] = st[a]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ a ≠ b → (st -- b)[a] = st[a]
Proof step 6:
a ≠ a0, ∀ a, st. ¬ a ∈ s0 → (st \ s0)[a] = st[a] ⊦ ¬ a ∈ s0 ++ a0 → (st \ s0)[a] = st[a]

Rule argument

spec: store inst: name: Del-at seq: ⊦ a ≠ b → (st -- b)[a] = st[a] subst: [a, b, st] → [a, a0, st \ s0] flags: rewrite

Additional information

Used simplifier rules: lookupisempty: ⊦ (st -- a)[a] = (∅)[a]; from specification store%add: ⊦ ¬ a ∈ s ++ b ↔ a ≠ b ∧ ¬ a ∈ s; from specification set-basic Used terms: a, a0, st \ s0