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

remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, pmaxino ≠ 0, fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, inv(gstore0), inv(gstore \ jro), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-inj(fi0), ri-inj(fi), pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore0, fi.lebs ⊆ dom gstore, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ [index_index_remove#(key, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; adr, jvalid, fi)] ( ri-inj(fi) → ⟪if jvalid then let n = ? in {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)}⟫ ( fi.inos < jmaxino ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 10:
gstore = gstore1, gstore0 = gstore2, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi), refsize-cons(gstore1, range fi0), ri-inj(fi), ri-inj(fi0), pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore2, fi0.lebs ⊆ dom gstore1, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ [jvalid := key ∈ fi; if jvalid then {adr := fi[key]; fi := fi -- key} else adr := ?] ( ri-inj(fi) → ⟪if jvalid then let n = ? in {index_get_gblock_refsize#(adr.lnum, fi, fi0, jro, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi, fi0, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)}⟫ ( fi.inos < jmaxino ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro)), pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: index_index_remove# (KEY, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; OLDADR, EXISTS, PRI ) {EXISTS := KEY ∈ PRI; if EXISTS then {OLDADR := PRI[KEY]; PRI := PRI -- KEY} else OLDADR := ? };