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Proof step 108 from proof inv-store (previous step)

jvalid ↔ key ∈ fi2, gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), adr0 = @(m0, m1, m2), fi = fi2[key, adr0], fi1 = fi2, gstore = gstore2, gstore0 = gstore3, gstore1 = gstore3, jro = jro0, jro2 = jro0, ¬ jvalid, remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, fi0.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore2), inv(gstore3 \ jro0), key-cons(key, nd), refsize-cons(gstore2, range fi0), refsize-cons(gstore3, range fi2), ri-inj(fi2[key, adr0]), ri-inj(fi2), ri-inj(fi0), @(m0, m1, m2) ∈ gstore3, pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ ⟪index_get_gblock_refsize#(m0, fi, fi0, jro, gstore3, gstore2, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m0, n + m2, fi, fi0, jro, gstore2, nx, pmaxino, p_os, jvalid0; gstore3); jmaxino := max(key.ino + 1, jmaxino)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi1.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0)) ∧ fi1[key, @(m0, m1, m2)].lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi1[key, @(m0, m1, m2)]) ∧ inv(gstore3 \ jro0) ∧ dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0 ∧ gstore3 =○refsize gstore1 ∧ fi = fi1[key, @(m0, m1, m2)]), jmaxino = 0, pmaxino = 0, dups(nx), @(m0, m1, m2) ∈ fi2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 109:
gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi0.inos < pmaxino, inv(gstore3 \ jro0), inv(gstore2), key-cons(key, nd), refsize-cons(gstore3, range fi2), refsize-cons(gstore2, range fi0), ri-inj(fi0), ri-inj(fi2), ri-inj(fi2[key, @(m0, m1, m2)]), @(m0, m1, m2) ∈ gstore3, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore3, fi0.lebs ⊆ dom gstore2, ¬ dups(nx), ¬ @(m0, m1, m2) ∈ fi2, ¬ key ∈ fi2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ ⟪index_get_gblock_refsize#(m0, fi2[key, @(m0, m1, m2)], fi0, jro0, gstore3, gstore2, nx, pmaxino, p_os, jvalid0; ; n); gstore := gstore3; index_set_gblock_refsize#(m0, n + m2, fi2[key, @(m0, m1, m2)], fi0, jro0, gstore2, nx, pmaxino, p_os, jvalid0; gstore3); jmaxino := max(key.ino + 1, jmaxino)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0)) ∧ fi2.lebs ++ m0 ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi2 ++ @(m0, m1, m2)) ∧ inv(gstore3 \ jro0) ∧ dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0 ∧ gstore3 =○refsize gstore)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ri → range ri[key, adr] = range ri ++ adr; (s)% ⊦ @(m, m0, m1).lnum = m; (s)% ⊦ ¬ key ∈ ri → ri[key, adr].lebs = ri.lebs ++ adr.lnum; (s)