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Proof step 4 from proof repalyone-monotonic (previous step)

∀ key. key ∈ ri0 → key ∈ ri1 ⊦ dom replay-one(adr, fs[adr], ri0) ⊆ dom replay-one(adr, fs[adr], ri1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ks ⊆ ks0 ↔ (∀ key. key ∈ ks → key ∈ ks0)
Proof step 6:
∀ key. key ∈ ri0 → key ∈ ri1 ⊦ ∀ key. key ∈ dom replay-one(adr, fs[adr], ri0) → key ∈ dom replay-one(adr, fs[adr], ri1)

Rule argument

spec: set-basic, inst: node-index name: Subset seq: ⊦ ks ⊆ ks0 ↔ (∀ key. key ∈ ks → key ∈ ks0) subst: [ks0, ks] → [dom replay-one(adr, fs[adr], ri1), dom replay-one(adr, fs[adr], ri0)] flags: <all paths>

Additional information

Used terms: dom replay-one(adr, fs[adr], ri1), dom replay-one(adr, fs[adr], ri0)