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Proof step 2 from proof lebs-write-subseteq0 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m ∈ gstore, ri.lebs ⊆ dom gstore ⊦ ri[key, @(m, m1, m2)].lebs ⊆ dom gstore, ri[key, @(m, m1, m2)].lebs ⊆ ri.lebs

Rule argument

Additional information

Used simplifier rules: sub-ntrans-01: ⊦ ns ⊆ ns0 ∧ ¬ ns1 ⊆ ns0 → ¬ ns1 ⊆ ns; (forward) from specification set-basic[nat-set]