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Proof step 5 from proof rem-write-other (previous step)

a ∈ s ⊦ s = ∅, # s = 0, (a0 ∈ st[a, d] \ s ↔ a0 ∈ st \ s) ∧ (st[a, d] \ s)[a0] = (st \ s)[a0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ a ∈ s → (st \ s)[a] = st[a]
Proof step 7:
¬ a0 ∈ s, a ∈ s ⊦ s = ∅, # s = 0, (a0 ∈ st[a, d] \ s ↔ a0 ∈ st \ s) ∧ st[a, d][a0] = (st \ s)[a0]

Rule argument

spec: inst: name: Diff-get seq: ⊦ ¬ a ∈ s → (st \ s)[a] = st[a] subst: [a, s, st] → [a0, s, st[a, d]] flags: rewrite, current

Additional information

Used simplifier rules: Diff-mems-get: ⊦ a ∈ s → (st \ s)[a] = (∅)[a];%Diff-ext: ⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s; Used terms: a0, s, st[a, d]