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Proof step 87 from proof refine-gc (previous step)

# ax = # gndx0, gstore2[n1].gndlist = gndx0, gstore2[n1].ladrlist.to-adr(n1) = ax, boolvar ↔ jvalid4, gstore2[n1] = groupblock(gndx0, lax, m), ax = lax.to-adr(n1), ax = ax, ax1 = ax, fi2 = fi1, ginval0 = jro0, gndx0 = gndx0, gndx1 = gndx0, gstore3 = gstore2, gstore4 = gstore1, lnum0 = n1, maxino0 = pmaxino, ns0 = p_os, nx1 = nx, remove-refsize0(gstore1) = gstore1, ri0 = ri, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, ri.inos < jmaxino, jro1 < jmaxino, p_os < pmaxino, fi1.inos < pmaxino, inv(gstore1), inv(groupblock(gndx0, lax, m)), inv(gstore2 \ jro0), 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), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [gjournal_gc_referenced_nodes#(n1, ri, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid4; ax, gndx0; ndx, err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ndx = nodes(gstore3 ↓, ginval0)[referenced-adrs(ax1, ri0)]) → [log := abs-log(nx, gstore2 ↓); fs := nodes(gstore2 ↓, jro0); fi0 := fi1; fi := ri; if err = ESUCCESS then {gjournal_gc_copy#(jvalid1, fi0, gstore1, pmaxino, p_os; ndx, jvalid3, jmaxino0, jmaxino, fi, jro0, gstore2, nx, jvalid4; err); if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + n1.toString + " to journal head during GC")}; if err = ESUCCESS then index_sync#(fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid4, err); if err = ESUCCESS then index_deallocate_gnd#(n1, fi, fi0, gstore1, nx, pmaxino, p_os, jvalid4; jro0, gstore2; err)] ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi) → ⟨aubifs_core_journal_gc#(fi1, jro1.keys, p_os.keys; ri, fs, log; jvalid5)⟩ (fi = ri ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid5 → jvalid4)))), jmaxino = 0, m = 0, pmaxino = 0, dups(nx), n1 ∈ nx, n1 ∈ jro0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
# gstore2[n1].ladrlist = # gstore2[n1].gndlist, gstore2[n1].gndlist = gndx0, gstore2[n1] = groupblock(gstore2[n1].gndlist, gstore2[n1].ladrlist, m), ax = gstore2[n1].ladrlist.to-adr(n1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, m ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, p_os < pmaxino, jro1 < jmaxino, ri.inos < jmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore2[n1]), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), 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, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ¬ dups(nx), ¬ n1 ∈ jro0, ¬ n1 ∈ nx, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid4 ⊦ [gjournal_gc_referenced_nodes#(n1, ri, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid4; ax, gndx0; ndx, err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ndx = nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri)]) → [log := abs-log(nx, gstore2 ↓); fs := nodes(gstore2 ↓, jro0); fi0 := fi1; fi := ri; if err = ESUCCESS then {gjournal_gc_copy#(jvalid1, fi0, gstore1, pmaxino, p_os; ndx, jvalid3, jmaxino0, jmaxino, fi, jro0, gstore2, nx, jvalid4; err); if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + n1.toString + " to journal head during GC")}; if err = ESUCCESS then index_sync#(fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid4, err); if err = ESUCCESS then index_deallocate_gnd#(n1, fi, fi0, gstore1, nx, pmaxino, p_os, jvalid4; jro0, gstore2; err)] ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi) → ⟨aubifs_core_journal_gc#(fi1, jro1.keys, p_os.keys; ri, fs, log; jvalid5)⟩ (fi = ri ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid5 → jvalid4))))

Rule argument

Additional information

Used simplifier rules: fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base% ⊦ # lax.to-adr(n) = # lax; (s)% ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1; (s)