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Proof step 2 from proof adr-in-ri-leb-notin-ginval (previous step)

ri[key] = @(m0, m1, m2), ri-cons(ri, nodes(gstore ↓, ginval)), key ∈ ri ⊦ m0 ∈ ginval ↔ false

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
ri[key] = @(m0, m1, m2), ri-cons(ri, nodes(gstore ↓, ginval)), m0 ∈ ginval, key ∈ ri ⊦ # ginval = 0, ginval = ∅

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%ne-01: ⊦ n ∈ ns → ns ≠ ∅; (forward) from specification set-basic[nat-set]