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Proof step 2 from proof Diff-mems-get (previous step)

a ∈ s ⊦ s = ∅, (st \ s)[a] = (∅)[a], # s = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ a ∈ st → st[a] = (∅)[a]

Rule argument

spec: store inst: name: notmemlookup seq: ⊦ ¬ a ∈ st → st[a] = (∅)[a] subst: [a, st] → [a, st \ s] flags: rewrite

Additional information

Used simplifier rules: Diff-ext: ⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s; Used terms: a, st \ s