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Proof step 7 from proof adr-in-ri-notin-nodes (previous step)

∀ key. key ∈ ri → ri[key] ∈ nodes(gstore, ginval) ∧ key-cons(key, nodes(gstore, ginval)[ri[key]]), ∃ key. key ∈ ri ∧ ri[key] = adr ⊦ adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
key ∈ ri, ∀ key0. key0 ∈ ri → ri[key0] ∈ gstore ∧ ¬ ri[key0].lnum ∈ ginval ∧ key-cons(key0, nodes(gstore, ginval)[ri[key0]]) ⊦ ri[key] ∈ gstore ∧ ¬ ri[key].lnum ∈ ginval

Rule argument

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);