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Proof step 7 from proof rem-write (previous step)

⊦ a0 = a, a ∈ s, (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

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;%Diff-ext: ⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s;%Diff-get: ⊦ ¬ a ∈ s → (st \ s)[a] = st[a];%in-neq: ⊦ a ≠ b → (a ∈ st[b, d] ↔ a ∈ st); from specification store%At-other: ⊦ a ≠ b → st[b, d][a] = st[a]; from specification store%ne-01: ⊦ a ∈ s → s ≠ ∅; (forward) from specification set-basic Used terms: a0, s, st[a, d]