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Proof step 408 from proof refine-gc (previous step)

gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = jro0 ∪ dom gstore2, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, p_os < pmaxino, jro1 < jmaxino, ri.inos < jmaxino, inv(gstore2 \ jro0), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2 -- n1, range ri), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(ri), n1 ∈ gstore2, n1 ∈ gstore1, n1 ∈ jro0 ∪ dom gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2 -- n1, jro0 ++ n1), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid0 ⊦ #((dom nodes(gstore2 ↓, jro0) | n1) ∩ range ri) = 0, #(jro0 ∪ dom gstore2) = 0, jmaxino = 0, pmaxino = 0, (dom nodes(gstore2 ↓, jro0) | n1) ∩ range ri = ∅, jro0 ∪ dom gstore2 = ∅, dups(nx), n1 ∈ nx, ∃ adr. adr.lnum = n1 ∧ adr ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 409:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 410:
gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = jro0 ∪ dom gstore2, p_os.keys.inodes?, jro1.keys.inodes?, ri.inos < jmaxino, jro1 < jmaxino, p_os < pmaxino, fi1.inos < pmaxino, inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), refsize-cons(gstore2 -- n1, range ri), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri), ri-inj(fi1), n1 ∈ jro0 ∪ dom gstore2, n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid5 → jvalid0, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2 -- n1, jro0 ++ n1) ⊦ #(jro0 ∪ dom gstore2) = 0, #((dom nodes(gstore2 ↓, jro0) | n1) ∩ range ri) = 0, jmaxino = 0, pmaxino = 0, jro0 ∪ dom gstore2 = ∅, dups(nx), n1 ∈ nx, ∀ adr. adr ∈ (dom nodes(gstore2 ↓, jro0) | n1) ∩ range ri ↔ adr ∈ ∅, ∃ adr. adr.lnum = n1 ∧ adr ∈ ri

Rule argument

spec: set-basic, inst: node-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [∅, (dom nodes(gstore2 ↓, jro0) | n1) ∩ range ri] flags: <all paths>

Additional information

Used terms: ∅, (dom nodes(gstore2 ↓, jro0) | n1) ∩ range ri