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Proof step 4 from proof refine-lookup (previous step)

jvalid ↔ jvalid2, jvalid2 ↔ jvalid3, fi = fi1, fi0 = ri, gstore = gstore1, gstore0 = gstore2, jro = jro0, nd = nd0, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < 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, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid4 → jvalid0 ⊦ ⟪if ri-cons(fi0, nodes(gstore0 ↓, jro)) then let adr = ? in {index_index_lookup#(key, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; jvalid, adr; err); if err = ESUCCESS ∧ jvalid then let gnd = ? in {index_read_gnd#(adr, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; gnd; err); if err = ESUCCESS then nd := gnd.nd}} else abort⟫ ⟨aubifs_core_index_lookup#(key, ri, fi1, jro1.keys, p_os.keys, nodes(gstore2 ↓, jro0), abs-log(nx, gstore2 ↓), jvalid4; jvalid3, nd0; err0)⟩ ((jvalid4 → jvalid0) ∧ (jvalid ↔ jvalid3) ∧ nd = nd0 ∧ err = err0), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 5:
jvalid2 ↔ jvalid3, jvalid ↔ jvalid2, fi = fi1, fi0 = ri, gstore = gstore1, gstore0 = gstore2, jro = jro0, nd = nd0, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < 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, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid4 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟪let adr = ? in {index_index_lookup#(key, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; jvalid, adr; err); if err = ESUCCESS ∧ jvalid then let gnd = ? in {index_read_gnd#(adr, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; gnd; err); if err = ESUCCESS then nd := gnd.nd}}⟫ ⟨aubifs_core_index_lookup#(key, ri, fi1, jro1.keys, p_os.keys, nodes(gstore2 ↓, jro0), abs-log(nx, gstore2 ↓), jvalid4; jvalid3, nd0; err0)⟩ ((jvalid4 → jvalid0) ∧ (jvalid ↔ jvalid3) ∧ nd = nd0 ∧ err = err0), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ri-cons(ri, fs) → ( ri-cons(ri0, fs0) ↔ (∀ key. (key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]])) → key ∈ ri0 → ri0[key] ∈ fs0 ∧ key-cons(key, fs0[ri0[key]]))); (ss)