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Proof step 11 from proof rem-write-other (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ a ≠ b → st[b, d][a] = st[a]

Rule argument

spec: store name: At-other seq: ⊦ a ≠ b → st[b, d][a] = st[a] subst: [a, d, b, st] → [a0, d, a, st] flags: <all paths>

Additional information

Used simplifier rules: ⊦ a ∈ st[b, d] ↔ a = b ∨ a ∈ st; (ws) Used terms: a0, d, a, st