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Proof step 9 from proof inv-store (previous step)

gstore[adr1] = mkgnode(nd, m, boolvar, boolvar0), fi1 = fi, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro1 < jmaxino, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), key-cons(key, nd), refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), ri-inj(fi), ri-inj(fi0), adr1 ∈ gstore, pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, ¬ dups(nx), ¬ adr1 ∈ fi, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪index_index_store#(key, adr1, fi0, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid0; adr, jvalid, fi); let n = ? in {jro := jro0; gstore1 := gstore; if jvalid then {index_get_gblock_refsize#(adr.lnum, fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid0; gstore)}; index_get_gblock_refsize#(adr1.lnum, fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(adr1.lnum, n + adr1.size, fi, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid0; gstore)}; 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, gstore, jro0)) ∧ fi1[key, adr1].lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi1[key, adr1]) ∧ inv(gstore \ jro0) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro0 ∧ ri-inj(fi1[key, adr1]) ∧ gstore =○refsize gstore1 ∧ fi = fi1[key, adr1])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
gstore[adr1] = mkgnode(nd, m, boolvar, boolvar0), adr1 = @(m0, m1, m2), fi1 = fi, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore0), inv(gstore \ jro0), key-cons(key, nd), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-inj(fi0), ri-inj(fi), adr1 ∈ gstore, pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore0, fi.lebs ⊆ dom gstore, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪index_index_store#(key, adr1, fi0, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid0; adr, jvalid, fi); let n = ? in {jro := jro0; gstore1 := gstore; if jvalid then {index_get_gblock_refsize#(adr.lnum, fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid0; gstore)}; index_get_gblock_refsize#(m0, fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m0, n + m2, fi, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid0; gstore)}; 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, gstore, jro0)) ∧ fi1[key, adr1].lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi1[key, adr1]) ∧ inv(gstore \ jro0) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro0 ∧ ri-inj(fi1[key, adr1]) ∧ gstore =○refsize gstore1 ∧ fi = fi1[key, adr1]), jmaxino = 0, pmaxino = 0, dups(nx), adr1 ∈ 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] → [adr1, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: adr1, m0, m1, m2