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Proof step 3 from proof lebs-write-subseteq0 (previous step)

m ∈ gstore, ri.lebs ⊆ dom gstore ⊦ ri[key, @(m, m1, m2)].lebs ⊆ dom gstore, ri[key, @(m, m1, m2)].lebs ⊆ ri.lebs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0)
Proof step 5:
m ∈ gstore, ri.lebs ⊆ dom gstore ⊦ ri[key, @(m, m1, m2)].lebs ⊆ ri.lebs, ∀ n. n ∈ ri[key, @(m, m1, m2)].lebs → n ∈ dom gstore

Rule argument

spec: set-basic, inst: nat-set name: Subset seq: ⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0) subst: [ns0, ns] → [dom gstore, ri[key, @(m, m1, m2)].lebs] flags: <all paths>

Additional information

Used terms: dom gstore, ri[key, @(m, m1, m2)].lebs