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Proof step 5 from proof nodes-remove-refsize0 (previous step)

dom remove-refsize0(gstore) ∩ ginval = ∅ ⊦ ∀ adr. (adr ∈ nodes(remove-refsize0(gstore), ∅) ↔ adr ∈ nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval)) ∧ ( adr ∈ nodes(remove-refsize0(gstore), ∅) → nodes(remove-refsize0(gstore), ∅)[adr] = (nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval))[adr])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
dom remove-refsize0(gstore) ∩ ginval = ∅ ⊦ (adr ∈ remove-refsize0(gstore) ↔ adr ∈ nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval)) ∧ (adr ∈ remove-refsize0(gstore) → nodes(remove-refsize0(gstore), ∅)[adr] = (nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval))[adr])

Rule argument

Additional information

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