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Proof step 51 from proof inv-gc (previous step)

# ax = # gndx0, gstore2[n1].gndlist = gndx0, gstore2[n1].ladrlist.to-adr(n1) = ax, boolvar ↔ jvalid, gstore2[n1] = groupblock(gndx0, lax, m), ax = lax.to-adr(n1), ax = ax, ax1 = ax, fi0 = fi1, ginval0 = jro0, gndx0 = gndx0, gndx1 = gndx0, gstore3 = gstore2, gstore4 = gstore1, lnum0 = n1, maxino0 = pmaxino, ns0 = p_os, nx1 = nx, remove-refsize0(gstore1) = gstore1, ri0 = fi2, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore1), inv(groupblock(gndx0, lax, m)), inv(gstore2 \ jro0), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(fi2), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [gjournal_gc_referenced_nodes#(n1, fi2, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid; ax, gndx0; ndx, err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ndx = nodes(gstore3 ↓, ginval0)[referenced-adrs(ax1, ri0)]) → ⟪if err = ESUCCESS then {gjournal_gc_copy#(jvalid1, fi1, gstore1, pmaxino, p_os; ndx, jvalid4, jmaxino0, jmaxino, fi2, jro0, gstore2, nx, jvalid; err); if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + n1.toString + " to journal head during GC")}; if err = ESUCCESS then index_sync#(fi2, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid, err); if err = ESUCCESS then index_deallocate_gnd#(n1, fi2, fi1, gstore1, nx, pmaxino, p_os, jvalid; jro0, gstore2; err)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi2.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi2) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi2))), jmaxino = 0, m = 0, pmaxino = 0, dups(nx), n1 ∈ nx, n1 ∈ jro0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
# gstore2[n1].ladrlist = # gstore2[n1].gndlist, gstore2[n1].gndlist = gndx0, gstore2[n1] = groupblock(gstore2[n1].gndlist, gstore2[n1].ladrlist, m), ax = gstore2[n1].ladrlist.to-adr(n1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, m ≠ 0, pmaxino ≠ 0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore2[n1]), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), ¬ n1 ∈ jro0, ¬ n1 ∈ nx, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [gjournal_gc_referenced_nodes#(n1, fi2, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid; ax, gndx0; ndx, err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ndx = nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), fi2)]) → ⟪if err = ESUCCESS then {gjournal_gc_copy#(jvalid1, fi1, gstore1, pmaxino, p_os; ndx, jvalid4, jmaxino0, jmaxino, fi2, jro0, gstore2, nx, jvalid; err); if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + n1.toString + " to journal head during GC")}; if err = ESUCCESS then index_sync#(fi2, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid, err); if err = ESUCCESS then index_deallocate_gnd#(n1, fi2, fi1, gstore1, nx, pmaxino, p_os, jvalid; jro0, gstore2; err)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi2.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi2) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi2)))

Rule argument

Additional information

Used simplifier rules: fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base% ⊦ # lax.to-adr(n) = # lax; (s)% ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1; (s)