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Proof step 20 from proof refine-lookup (previous step)

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?, 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), key ∈ ri, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid4 → jvalid0 ⊦ ⟪index_read_gnd#(ri[key], ri, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; gnd; err0); nd := nd0; if err0 = 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; err1)⟩ ((jvalid4 → jvalid0) ∧ jvalid3 ∧ nd = nd0 ∧ err0 = err1)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 21:
jvalid ↔ jvalid0, adr = ri[key], fi = fi1, fi0 = ri, gstore = gstore1, gstore0 = gstore2, jro = jro0, 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), key ∈ ri, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid4 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟪if adr ∈ gstore0 ∧ ¬ adr.lnum ∈ jro then {fail_or_success#(; ; err); if err = ESUCCESS then gnd := gstore0[adr] else gnd := ?} else abort; nd := nd0; err0 := err; if err0 = 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; err1)⟩ ((jvalid4 → jvalid0) ∧ jvalid3 ∧ nd = nd0 ∧ err0 = err1), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: index_read_gnd# (ADR, PRI, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; GND ; ERR ) {if ADR ∈ PSTORE ∧ ¬ ADR.lnum ∈ PINVAL then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then GND := PSTORE[ADR] else GND := ?} else abort };