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Proof step 35 from proof refine-lookup (previous step)

ri[key] = @(m, m0, m1), 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), @(m, m0, m1) ∈ gstore2, key ∈ ri, m ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ¬ dups(nx), ¬ m ∈ jro0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid4 → jvalid0 ⊦ ⟨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 ∧ gstore2[ri[key]].nd = nd0 ∧ ESUCCESS = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
ri[key] = @(m, m0, m1), gstore2[ri[key]] = mkgnode(nd, m2, boolvar, boolvar0), 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), m ∈ gstore2, key ∈ ri, @(m, m0, m1) ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid4 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟨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 ∧ ESUCCESS = err1), jmaxino = 0, pmaxino = 0, dups(nx), m ∈ jro0

Rule argument

spec: groupnode name: elim seq: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0) subst: [gnd, nd, m, boolvar, boolvar0] → [gstore2[ri[key]], nd, m2, boolvar, boolvar0]

Additional information

Used simplifier rules: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0); (elim) Used terms: gstore2[ri[key]], nd, m2, boolvar, boolvar0