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Proof step 5 from proof refine-commit (previous step)

p_os.keys = fo, jvalid ↔ jvalid0, fi = fi2, fi0 = ri, fi2 = fi1, fs = nodes(gstore2 ↓, jro0), gstore = gstore1, gstore0 = gstore2, jro1 = jro, log = abs-log(nx, gstore2 ↓), remove-refsize0(gstore1) = gstore1, dom remove-refsize0(gstore0) ∩ jro0 = ∅, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro.keys.inodes?, p_os.keys.inodes?, jro < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), 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, fi0.lebs ⊆ dom remove-refsize0(gstore0), ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟪index_sync#(fi0, fi, jro0, gstore0, gstore, nx, pmaxino, p_os; ; jvalid, err); if err = ESUCCESS then let jro = jro1 in index_commit#(jmaxino, fi0, jvalid; jro, jro0, gstore0, fi, gstore, nx, pmaxino, p_os; err)⟫ ⟨aubifs_core_commit#(ri, jro.keys; fs, fi1, fo, log; jvalid2, err0)⟩ (p_os.keys = fo ∧ fi = fi1 ∧ log = abs-log(nx, gstore0 ↓) ∧ fs = nodes(gstore0 ↓, jro0) ∧ (jvalid2 → jvalid) ∧ err = err0), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom remove-refsize0(gstore2) ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, p_os.keys.inodes?, jro.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv(gstore1), inv(gstore2 \ jro0), 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), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 → jvalid0 ⊦ ⟪index_sync#(ri, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid0, err); log := abs-log(nx, gstore2 ↓); gstore0 := gstore2; fs := nodes(gstore2 ↓, jro0); fi := fi1; fo := p_os.keys; if err = ESUCCESS then let jro2 = jro in index_commit#(jmaxino, ri, jvalid0; jro2, jro0, gstore0, fi, gstore1, nx, pmaxino, p_os; err)⟫ ⟨aubifs_core_commit#(ri, jro.keys; fs, fi1, fo, log; jvalid2, err0)⟩ (p_os.keys = fo ∧ fi = fi1 ∧ log = abs-log(nx, gstore0 ↓) ∧ fs = nodes(gstore0 ↓, jro0) ∧ (jvalid2 → jvalid0) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ri-cons(ri, nodes(gstore ↓, ginval)) ∧ refsize-cons(gstore, range ri) ∧ inv(gstore \ ginval) → ri.lebs ⊆ dom remove-refsize0(gstore); (s)