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Proof step 12 from proof nodes-remove-refsize0 (previous step)

gstore[m] = groupblock(gndx, lax, m2), dom remove-refsize0(gstore) ∩ ginval = ∅ ⊦ (@(m, m0, m1) ∈ remove-refsize0(gstore) ↔ @(m, m0, m1) ∈ gstore ∧ ¬ m ∈ ginval ∧ m2 ≠ 0) ∧ ( @(m, m0, m1) ∈ remove-refsize0(gstore) → nodes(remove-refsize0(gstore), ∅)[@(m, m0, m1)] = (nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval))[@(m, m0, m1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist
Proof step 14:
gstore[m] = groupblock(gndx, lax, m2), dom remove-refsize0(gstore) ∩ ginval = ∅ ⊦ ( @(m, m0, m1).lnum ∈ remove-refsize0(gstore) ∧ @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ remove-refsize0(gstore)[@(m, m0, m1).lnum].ladrlist ↔ @(m, m0, m1) ∈ gstore ∧ ¬ m ∈ ginval ∧ m2 ≠ 0) ∧ ( @(m, m0, m1).lnum ∈ remove-refsize0(gstore) ∧ @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ remove-refsize0(gstore)[@(m, m0, m1).lnum].ladrlist → nodes(remove-refsize0(gstore), ∅)[@(m, m0, m1)] = (nodes(gstore, ginval) \ refsize0-addresses(gstore \ ginval))[@(m, m0, m1)])

Rule argument

spec: ablock-store-inv, inst: group-store name: in seq: ⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist subst: [gstore, adr] → [remove-refsize0(gstore), @(m, m0, m1)] flags: <all paths>

Additional information

Used terms: remove-refsize0(gstore), @(m, m0, m1)