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Proof step 27 from proof recovery (previous step)

jvalid1 ↔ jvalid, jvalid ↔ true, err = err0, err = ESUCCESS, fi = fi1, fi0 = fi2, fi1 = fi3, fi2 = fi1, gstore = gstore3, gstore0 = crash(gstore2, gstore3, jro4, nx1), gstore1 = gstore, jmaxino = pmaxino, jmaxino1 = pmaxino, jro = jro4, jro0 = p_os, jro2 = jro, jro3 = p_os, ks = ks0, log = ax, nx = nx1, nx0 = nx, nx2 = nx0, nx3 = nx, p_os = jro1, pmaxino = jmaxino0, remove-refsize0(gstore3) = gstore3, elems nx1 ∩ jro4 = ∅, dom gstore3 ∪ elems nx1 = dom gstore2 ∪ jro4, jro5.keys.inodes?, jro1.keys.inodes?, jro5 < jmaxino3, jro1 < jmaxino0, ri0.inos < jmaxino3, fi3.inos < jmaxino0, inv(gstore2 \ jro4), inv(gstore3), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro4)), refsize-cons(gstore2, range ri0), refsize-cons(gstore3, range fi3), ri-inj(ri0), ri-inj(fi3), jmaxino0 ≤ jmaxino3, ri0.lebs ⊆ dom gstore2, fi3.lebs ⊆ dom gstore3, jvalid8 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro4), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪gjournal_restore_log#(nx2, fi0, fi, jro2, gstore0, gstore1, nx3, jmaxino1, jro3, jvalid1; log; err); ks := jro0.keys⟫ ( ( err = ESUCCESS → (∃ ro. ⟨log0 := abs-log(nx1, gstore2 ↓); fs0 := nodes(gstore2 ↓, jro4); fo0 := jro1.keys; aubifs_core_recover#(jvalid2; ax, ks0, fi3, ro, fo0, log0, fs0; ri, jvalid, err1)⟩ ( jro0.keys = ro ∧ jro3.keys = fo0 ∧ fi0 = ri ∧ fi = fi3 ∧ log0 = abs-log(nx3, gstore0 ↓) ∧ fs0 = nodes(gstore0 ↓, jro2) ∧ (jvalid → jvalid1) ∧ log = ax ∧ ks = ks0 ∧ ESUCCESS = err1))) ∧ ( err ≠ ESUCCESS → (∀ ri, fi, ro, fo, fs, log0, jvalid0. ⟨aubifs_core_recover#(jvalid2; ax, ks0, fi5, ro1, fo1, log, fs1; ri1, jvalid7, err1)⟩ (ri = ri1 ∧ fi = fi5 ∧ ro = ro1 ∧ fo = fo1 ∧ fs = fs1 ∧ log0 = ax ∧ (jvalid0 ↔ jvalid7) ∧ log = ax ∧ ks = ks0 ∧ err = err1)))), jmaxino0 = 0, jmaxino3 = 0, dups(nx1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
log = ax, remove-refsize0(gstore3) = gstore3, elems nx1 ∩ jro4 = ∅, dom gstore3 ∪ elems nx1 = dom gstore2 ∪ jro4, jmaxino0 ≠ 0, jmaxino3 ≠ 0, jro1.keys.inodes?, jro5.keys.inodes?, fi3.inos < jmaxino0, ri0.inos < jmaxino3, jro1 < jmaxino0, jro5 < jmaxino3, inv(gstore3), inv(gstore2 \ jro4), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro4)), refsize-cons(gstore3, range fi3), refsize-cons(gstore2, range ri0), ri-inj(fi3), ri-inj(ri0), jmaxino0 ≤ jmaxino3, fi3.lebs ⊆ dom gstore3, ri0.lebs ⊆ dom gstore2, ¬ dups(nx1), jvalid8 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro4) ⊦ ⟪gjournal_restore_log#(nx1, fi3, fi3, jro4, crash(gstore2, gstore3, jro4, nx1), gstore3, nx1, jmaxino0, jro1, true; log; err); ks := jro1.keys⟫ ( ( err = ESUCCESS → (∃ ro. ⟨log0 := abs-log(nx1, gstore2 ↓); fs0 := nodes(gstore2 ↓, jro4); fo0 := jro1.keys; fi1 := fi3; fi0 := fi3; aubifs_core_recover#(jvalid2; ax, ks0, fi3, ro, fo0, log0, fs0; ri, jvalid, err1)⟩ ( jro1.keys = ro ∧ jro1.keys = fo0 ∧ fi1 = ri ∧ fi0 = fi3 ∧ log0 = abs-log(nx1, gstore2 ↓) ∧ fs0 = nodes(gstore2 ↓, jro4) ∧ log = ax ∧ ks = ks0 ∧ ESUCCESS = err1))) ∧ ( err ≠ ESUCCESS → (∀ ri, fi, ro, fo, fs, log0, jvalid0. ⟨aubifs_core_recover#(jvalid2; ax, ks0, fi5, ro1, fo1, log, fs1; ri1, jvalid7, err1)⟩ (ri = ri1 ∧ fi = fi5 ∧ ro = ro1 ∧ fo = fo1 ∧ fs = fs1 ∧ log0 = ax ∧ (jvalid0 ↔ jvalid7) ∧ log = ax ∧ ks = ks0 ∧ err = err1))))

Rule argument

Additional information

Used simplifier rules: ⊦ inv(gstore \ ginval) → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval) = nodes(gstore ↓, ginval); (s)%⊦ elems nx ∩ ginval = ∅ ∧ inv(gstore \ ginval) → abs-log(nx, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(nx, gstore ↓); (s)%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)