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Proof step 2 from proof rem-write-other (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a])
Proof step 4:
a ∈ s ⊦ s = ∅, ∀ a0. (a0 ∈ st[a, d] \ s ↔ a0 ∈ st \ s) ∧ (st[a, d] \ s)[a0] = (st \ s)[a0], # s = 0

Rule argument

spec: store inst: name: Extension seq: ⊦ st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a]) subst: [st2, st1] → [st \ s, st[a, d] \ s] flags: rewrite

Additional information

Used terms: st \ s, st[a, d] \ s