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Proof step 70 from proof refine-commit (previous step)

gstore2[m].ref-size = 0, remove-refsize0(gstore1) = gstore1, dom remove-refsize0(gstore2) ∩ jro3 = ∅, elems nx ∩ jro3 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro3, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro3), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro3)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro3)), ri-inj(ri), ri-inj(fi1), m ∈ gstore2, @(m, m0, m1) ∈ ri, @(m0, m1) ∈ prefixn(valid-group-nodes(gstore2[m].gndlist), gstore2[m].ladrlist), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro3) ⊦ #(refsize0-addresses((gstore2 \ jro3)↓) ∩ range ri) = 0, # refsize0-addresses((gstore2 \ jro3)↓) = 0, jmaxino = 0, pmaxino = 0, refsize0-addresses((gstore2 \ jro3)↓) = ∅, dups(nx), m ∈ jro3

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[m], gndx, lax, m2]

Additional information

Used simplifier rules: ⊦ gstore[n] = groupblock(gndx, lax, 0) ∧ n ∈ gstore ∧ ri-cons(ri, nodes(gstore ↓, ginval)) ∧ refsize-cons(gstore, range ri) ∧ inv(gstore \ ginval) → ¬ @(n, m0, m1) ∈ ri; (s)%⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore2[m], gndx, lax, m2