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Proof step 53 from proof refine-gc (previous step)

jvalid ↔ jvalid4, err = ESUCCESS, fi = ri, fi0 = fi1, fi2 = ri, fi3 = fi1, fs = nodes(gstore2 ↓, jro0), gstore = gstore1, gstore0 = gstore2, jro = jro0, lnum = n1, log = abs-log(nx, gstore2 ↓), n0 = lnum0, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, p_os < pmaxino, jro1 < jmaxino, ri.inos < jmaxino, inv(gstore2 \ jro0), inv(gstore1), 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 ∈ dom gstore0, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid4 ⊦ [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), n1 ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, 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), n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), ¬ n1 ∈ nx, jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [debug#("gjournal: garbage collecting LEB " + n1.toString); index_get_gblock_refsize#(n1, ri, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid4; ; n); log := abs-log(nx, gstore2 ↓); fs := nodes(gstore2 ↓, jro0); fi0 := fi1; fi := ri; err := ESUCCESS; if n ≠ 0 then let ax = [], gndx = [], ndx = [] in {index_read_gblock_nodes#(n1, fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid4; ax, gndx; err); if err ≠ ESUCCESS then debug#("gjournal: failed to read LEB " + n1.toString + " during GC") else gjournal_gc_referenced_nodes#(n1, 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 " + 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-in-gstore0: ⊦ n ∈ gstore ∧ ¬ n ∈ nx ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore0; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)