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Proof step 19 from proof inv-remove (previous step)

fi[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, pmaxino ≠ 0, 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 -- key), ri-inj(fi), ri-inj(fi0), key ∈ fi, m ∈ gstore2, pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore2, fi0.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪index_get_gblock_refsize#(m, fi -- key, fi0, jro, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m, n - m1, fi -- key, fi0, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)⟫ ( (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi -- @(m, m0, m1)) ∧ inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 20:
jvalid ↔ jvalid0, fi2[key] = @(m, m0, m1), fi = fi1, fi0 = fi2 -- key, gstore = gstore1, gstore0 = gstore2, lnum = m, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), ri-inj(fi2 -- key), m ∈ gstore2, key ∈ fi2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪if lnum ∈ gstore0 then n := gstore0[lnum].ref-size else abort; index_set_gblock_refsize#(m, n - m1, fi2 -- key, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)⟫ ( (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi2 -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi2 -- @(m, m0, m1)) ∧ 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_get_gblock_refsize# (LNUM, PRI, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; ; N ) {if LNUM ∈ PSTORE then N := PSTORE[LNUM].ref-size else abort};