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Proof step 26 from proof inv-store (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 27:
gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), fi[key] = @(m3, m4, m5), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore3 \ jro0), inv(gstore2), key-cons(key, nd), refsize-cons(gstore3, range fi), refsize-cons(gstore2, range fi0), ri-inj(fi0), ri-inj(fi), ri-inj(fi[key, @(m0, m1, m2)]), key ∈ fi, @(m0, m1, m2) ∈ gstore3, pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore3, fi0.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ ⟪index_get_gblock_refsize#(m3, fi[key, @(m0, m1, m2)], fi0, jro0, gstore3, gstore2, nx, pmaxino, p_os, jvalid0; ; n); gstore := gstore3; index_set_gblock_refsize#(m3, n - m5, fi[key, @(m0, m1, m2)], fi0, jro0, gstore2, nx, pmaxino, p_os, jvalid0; gstore3); index_get_gblock_refsize#(m0, fi[key, @(m0, m1, m2)], fi0, jro0, gstore3, gstore2, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m0, n + m2, fi[key, @(m0, m1, m2)], fi0, jro0, gstore2, nx, pmaxino, p_os, jvalid0; gstore3); jmaxino := max(key.ino + 1, jmaxino)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0)) ∧ fi[key, @(m0, m1, m2)].lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, (range fi -- fi[key]) ++ @(m0, m1, m2)) ∧ inv(gstore3 \ jro0) ∧ dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0 ∧ gstore3 =○refsize gstore), jmaxino = 0, pmaxino = 0, dups(nx), @(m0, m1, m2) ∈ fi

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] → [fi[key], m3, m4, m5]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: fi[key], m3, m4, m5