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Proof step 103 from proof refine-gc (previous step)

# lax = # gndx0, jvalid2 ↔ jvalid1, gstore2[n1] = groupblock(gndx0, lax, m0), fi = ri, fi = fi, fi2 = fi1, fi3 = fi, fs = nodes(gstore2 ↓, jro0), gstore2 = gstore2, gstore3 = gstore1, gstore4 = gstore2, jmaxino = jmaxino, jmaxino2 = jmaxino, jro0 = jro0, jro2 = jro1, jro3 = jro0, log = abs-log(nx, gstore2 ↓), ndx = nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)], ndx = ndx, ndx0 = ndx, nx = nx, nx1 = nx, p_os0 = p_os, pmaxino0 = pmaxino, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, ri.inos < jmaxino, jro1 < jmaxino, p_os < pmaxino, fi.inos < jmaxino, fi1.inos < pmaxino, inv(groupblock(gndx0, lax, m0)), inv(gstore1), inv(gstore2 \ jro0), inv-journal(nx, gstore2, gstore1, jro0), key-cons(ndx), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore2, range fi), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri), ri-inj(fi), ri-inj(fi1), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ndx.keys.toSet ⊆ dom fi, range fi ⊆ dom nodes(gstore2 ↓, jro0), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [gjournal_gc_copy#(jvalid1, fi1, gstore1, pmaxino, p_os; ndx, jvalid3, jmaxino0, jmaxino, fi, jro0, gstore2, nx, jvalid4; err)] ( jro2 < jmaxino ∧ pmaxino0 ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv-journal(nx, gstore2, gstore3, jro0) ∧ ri-inj(fi) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ jmaxino2 ≤ jmaxino ∧ dom gstore4 ⊆ dom gstore2 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore4 = ∅ ∧ (∃ ax, ndx, ndx1. ndx0 = ndx + ndx1 ∧ (err = ESUCCESS → ndx1 = []) ∧ new(ax, nodes(gstore4 ↓, jro3)) ∧ # ax = # ndx ∧ ¬ dups(ax) ∧ fi = fi3[ndx.keys, ax] ∧ nodes(gstore2 ↓, jro0) = nodes(gstore4 ↓, jro3)[ax, ndx] ∧ abs-log(nx, gstore2 ↓) = abs-log(nx1, gstore4 ↓) + ax) → [if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + n1.toString + " to journal head during GC"); fi0 := fi1; if err = ESUCCESS then index_sync#(fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid4, err); if err = ESUCCESS then index_deallocate_gnd#(n1, fi, fi0, gstore1, nx, pmaxino, p_os, jvalid4; jro0, gstore2; err)] ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi) → ⟨aubifs_core_journal_gc#(fi1, jro1.keys, p_os.keys; ri, fs, log; jvalid5)⟩ (fi = ri ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid5 → jvalid4)))), jmaxino = 0, m0 = 0, pmaxino = 0, dups(ndx.keys), dups(nx), n1 ∈ nx, n1 ∈ jro0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 104:
# lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), fi = ri, fs = nodes(gstore2 ↓, jro0), gstore4 = gstore2, jmaxino2 = jmaxino, jro3 = jro0, log = abs-log(nx, gstore2 ↓), ndx = nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)], ndx0 = nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)], nx1 = nx, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, m0 ≠ 0, pmaxino ≠ 0, p_os.keys.inodes?, jro1.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(groupblock(gndx0, lax, m0)), inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri), ri-inj(fi1), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range ri ⊆ dom nodes(gstore2 ↓, jro0), ¬ dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys), ¬ dups(nx), ¬ n1 ∈ nx, ¬ n1 ∈ jro0, jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [gjournal_gc_copy#(jvalid1, fi1, gstore1, pmaxino, p_os; ndx, jvalid3, jmaxino0, jmaxino, fi, jro0, gstore2, nx, jvalid4; err)] ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ jmaxino2 ≤ jmaxino ∧ dom gstore4 ⊆ dom gstore2 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore4 = ∅ ∧ (∃ ax, ndx, ndx1. ndx0 = ndx + ndx1 ∧ (err = ESUCCESS → ndx1 = []) ∧ new(ax, nodes(gstore4 ↓, jro3)) ∧ # ax = # ndx ∧ ¬ dups(ax) ∧ fi = ri[ndx.keys, ax] ∧ nodes(gstore2 ↓, jro0) = nodes(gstore4 ↓, jro3)[ax, ndx] ∧ abs-log(nx, gstore2 ↓) = abs-log(nx1, gstore4 ↓) + ax) → [if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + n1.toString + " to journal head during GC"); fi0 := fi1; if err = ESUCCESS then index_sync#(fi, fi0, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid4, err); if err = ESUCCESS then index_deallocate_gnd#(n1, fi, fi0, gstore1, nx, pmaxino, p_os, jvalid4; jro0, gstore2; err)] ( (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 → ⟨aubifs_core_journal_gc#(fi1, jro1.keys, p_os.keys; ri, fs, log; jvalid5)⟩ (fi = ri ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid5 → jvalid4))))

Rule argument

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)% ⊦ ri-cons(ri, fs) → key-cons(fs[referenced-adrs(ax, ri)]); (s)% ⊦ ri-cons(ri, fs) → fs[referenced-adrs(ax, ri)].keys.toSet ⊆ dom ri; (s)