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Proof step 122 from proof refine-commit (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro.keys.inodes?, p_os.keys.inodes?, jro < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri), ri-inj(fi1), n ∈ gstore2, n ∈ jro0, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ #(dom remove-refsize0(gstore2) ∩ jro0) = 0, # jro0 = 0, gstore2[n].ref-size = 0, jmaxino = 0, jro0 = ∅, pmaxino = 0, dups(nx)

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore2[n], gndx, lax, m]

Additional information

Used simplifier rules: refsize-nonzero-notin-ginval: ⊦ gstore[n] = groupblock(gndx, lax, m2) ∧ n ∈ gstore ∧ m2 ≠ 0 ∧ refsize-cons(gstore, range ri) ∧ ri-cons(ri, nodes(gstore ↓, ginval)) ∧ inv(gstore \ ginval) → ¬ n ∈ ginval; (forward) from specification gjournal-abs%⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore2[n], gndx, lax, m