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Proof step 9 from proof nodes-remove-refsize0 (previous step)

dom remove-refsize0(gstore) ∩ ginval = ∅ ⊦ (adr ∈ remove-refsize0(gstore) ↔ adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval ∧ (¬ adr ∈ gstore \ ginval ∨ gstore[adr.lnum].ref-size ≠ 0)) ∧ (adr ∈ remove-refsize0(gstore) → nodes(remove-refsize0(gstore), ∅)[adr] = (nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval))[adr])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
adr = @(m, m0, m1), dom remove-refsize0(gstore) ∩ ginval = ∅ ⊦ (adr ∈ remove-refsize0(gstore) ↔ adr ∈ gstore ∧ ¬ m ∈ ginval ∧ (¬ adr ∈ gstore \ ginval ∨ gstore[m].ref-size ≠ 0)) ∧ (adr ∈ remove-refsize0(gstore) → nodes(remove-refsize0(gstore), ∅)[adr] = (nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval))[adr])

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [adr, m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: adr, m, m0, m1