[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 98 from proof refine-gc (previous step)

# lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), fi = ri, fs = nodes(gstore2 ↓, jro0), log = abs-log(nx, gstore2 ↓), ndx = nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)], remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, m0 ≠ 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(groupblock(gndx0, lax, m0)), 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 ∈ nx, ¬ n1 ∈ jro0, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid4 ⊦ [gjournal_gc_copy#(jvalid1, fi1, 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"); fi0 := fi1; 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)))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: gjournal-asm name: inv-gc-copy seq: jro < jmaxino, p_os < pmaxino, pmaxino ≤ jmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, jmaxino ≠ 0, pmaxino ≠ 0, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), inv-journal(nx, gstore, gstore0, jro0), ri-inj(fi), ri-inj(fi0), ndx.keys.toSet ⊆ dom fi, ¬ dups(ndx.keys), range fi ⊆ dom nodes(gstore ↓, jro0), key-cons(ndx), jmaxino0 = jmaxino, gstore1 = gstore, nx0 = nx, ndx2 = ndx, jro1 = jro0, fi1 = fi ⊦ ⟪gjournal_gc_copy# (jvalid0, fi0, gstore0, pmaxino, p_os ; ndx, jvalid, jmaxino1, jmaxino, fi, jro0, gstore, nx, jvalid1 ; err)⟫ ( jro < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro0) ∧ ri-inj(fi) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ jmaxino0 ≤ jmaxino ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ (∃ ax, ndx0, ndx1. ndx2 = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = []) ∧ new(ax, nodes(gstore1 ↓, jro1)) ∧ # ax = # ndx0 ∧ ¬ dups(ax) ∧ fi = fi1[ndx0.keys, ax] ∧ nodes(gstore ↓, jro0) = nodes(gstore1 ↓, jro1)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax)) subst: [p_os, pmaxino, gstore0, fi0, jvalid0, jvalid1, nx, gstore, jro0, fi, jmaxino, jmaxino1, jvalid, ndx, err, jro, jmaxino0, gstore1, nx0, jro1, fi1, ndx2] → [p_os, pmaxino, gstore1, fi1, jvalid1, jvalid4, nx, gstore2, jro0, fi, jmaxino, jmaxino0, jvalid3, ndx, err, jro1, jmaxino, gstore2, nx, jro0, fi, ndx] flags: <all paths>

Additional information