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Proof step 23 from proof refine-lookup (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, 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, ri[key] ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), ¬ ri[key].lnum ∈ jro0, jvalid4 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then gnd := gstore2[ri[key]] else gnd := ?; 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
ri[key] = @(m, m0, m1), 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), ri[key] ∈ gstore2, key ∈ ri, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid4 → jvalid0 ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then gnd := gstore2[ri[key]] else gnd := ?; 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), m ∈ jro0

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [ri[key], m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: ri[key], m, m0, m1