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Proof step 20 from proof inv-truncate (previous step)

dom gstore = dom gstore3, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, # as0 ≠ 0, as0 ≠ ∅, pmaxino ≠ 0, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore =○refsize gstore3, inv(gstore \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n0, fi1)), @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, ¬ dups(nx), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ ⟪index_get_gblock_refsize#(m, fi1 \ datakeys(key, n0, fi1), fi2, jro, gstore, gstore1, nx, pmaxino, p_os, jvalid; ; n); index_set_gblock_refsize#(m, n - m1, fi1 \ datakeys(key, n0, fi1), fi2, jro, gstore1, nx, pmaxino, p_os, jvalid; gstore); as := as0 -- @(m, m0, m1)⟫ ( (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ dom gstore = dom gstore3 ∧ as ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅ ∧ as.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range(fi1 \ datakeys(key, n0, fi1)) ∪ as) ∧ inv(gstore \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore ∪ jro ∧ gstore =○refsize gstore3 ∧ # as < # as0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 21:
dom gstore2 = dom gstore3, fi = fi2, fi0 = fi1 \ datakeys(key, n0, fi1), gstore = gstore1, gstore0 = gstore2, lnum = m, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, p_os < pmaxino, fi1.inos < jmaxino, fi2.inos < pmaxino, gstore2 =○refsize gstore3, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore3, range fi1), refsize-cons(gstore1, range fi2), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), ri-inj(fi2), @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, as0.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪if lnum ∈ gstore0 then n := gstore0[lnum].ref-size else abort; index_set_gblock_refsize#(m, n - m1, fi1 \ datakeys(key, n0, fi1), fi2, jro, gstore1, nx, pmaxino, p_os, jvalid; gstore2); as := as0 -- @(m, m0, m1)⟫ ( (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ dom gstore2 = dom gstore3 ∧ as ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅ ∧ as.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as) ∧ inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro ∧ gstore2 =○refsize gstore3 ∧ # as < # as0), # as0 = 0, as0 = ∅, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: index_get_gblock_refsize# (LNUM, PRI, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; ; N ) {if LNUM ∈ PSTORE then N := PSTORE[LNUM].ref-size else abort};