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Proof step 10 from proof refine-gc (previous step)

remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, p_os < pmaxino, jro1 < jmaxino, ri.inos < jmaxino, inv(gstore \ jro0), inv(gstore0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ¬ dups(nx), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4 ⊦ [index_get_gc_block#(ri, fi1, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid4; lnum; err); log := abs-log(nx, gstore ↓); fs := nodes(gstore ↓, jro0); fi0 := fi1; fi := ri; if err = ESUCCESS then let n = ? in {debug#("gjournal: garbage collecting LEB " + lnum.toString); index_get_gblock_refsize#(lnum, fi, fi0, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid4; ; n); if n ≠ 0 then let ax = [], gndx = [], ndx = [] in {index_read_gblock_nodes#(lnum, fi, fi0, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid4; ax, gndx; err); if err ≠ ESUCCESS then debug#("gjournal: failed to read LEB " + lnum.toString + " during GC") else gjournal_gc_referenced_nodes#(lnum, fi, fi0, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid4; ax, gndx; ndx, err); if err = ESUCCESS then {gjournal_gc_copy# (jvalid1, fi0, gstore0, pmaxino, p_os; ndx, jvalid3, jmaxino0, jmaxino, fi, jro0, gstore, nx, jvalid4; err); if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + lnum.toString + " to journal head during GC")}}}; if err = ESUCCESS then index_sync#(fi, fi0, jro0, gstore, gstore0, nx, pmaxino, p_os; ; jvalid4, err); if err = ESUCCESS then index_deallocate_gnd#(lnum, fi, fi0, gstore0, nx, pmaxino, p_os, jvalid4; jro0, gstore; err)] ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro0 ∧ ri-inj(fi) → ⟨aubifs_core_journal_gc#(fi1, jro1.keys, p_os.keys; ri, fs, log; jvalid5)⟩ (fi = ri ∧ log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid5 → jvalid4)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 11:
jvalid ↔ jvalid4, fi = fi1, fi0 = ri, gstore = gstore1, gstore0 = gstore2, jro = jro0, n0 = lnum, remove-refsize0(gstore1) = gstore1, 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(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), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [err := ENOSPC or choose n with n ∈ dom gstore0 ∧ ¬ n ∈ nx in {n0 := n; err := ESUCCESS} ifnone err := ENOSPC; log := abs-log(nx, gstore2 ↓); fs := nodes(gstore2 ↓, jro0); fi0 := fi1; fi := ri; lnum := n0; if err = ESUCCESS then let n = ? in {debug#("gjournal: garbage collecting LEB " + lnum.toString); index_get_gblock_refsize#(lnum, fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid4; ; n); if n ≠ 0 then let ax = [], gndx = [], ndx = [] in {index_read_gblock_nodes#(lnum, fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid4; ax, gndx; err); if err ≠ ESUCCESS then debug#("gjournal: failed to read LEB " + lnum.toString + " during GC") else gjournal_gc_referenced_nodes#(lnum, fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid4; ax, gndx; ndx, err); 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 " + lnum.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#(lnum, 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, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: index_get_gc_block# (PRI, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; N ; ERR ) { ERR := ENOSPC or choose N0 with N0 ∈ dom PSTORE ∧ ¬ N0 ∈ PNL in {N := N0; ERR := ESUCCESS} ifnone ERR := ENOSPC };