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Proof step 6 from proof refine-add3 (previous step)

fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino1 ≠ 0, pmaxino ≠ 0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino1, p_os < pmaxino, jro1 < jmaxino1, inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), node-cons(nd2.key, nd2), node-cons(nd0.key, nd0), node-cons(nd3.key, nd3), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino1, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ¬ dups(nx), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4 ⊦ ⟪gjournal_journal_addn#(nd3 ' + nd0 ' + nd2 ', jvalid1, ri, fi1, gstore0, pmaxino, p_os; ax, jvalid3, jmaxino, jro0, gstore, nx, jvalid4; err); adr1 := adr5; adr0 := adr2; adr := adr4; if err = ESUCCESS then {adr1 := ax[0]; adr0 := ax[1]; adr := ax[2]}⟫ ⟨aubifs_core_journal_add3#(nd3, nd0, nd2, ri, fi1, jro1.keys, p_os.keys; adr5, adr2, adr4, fs, log; jvalid5, err0)⟩ (log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid5 → jvalid4) ∧ adr1 = adr5 ∧ adr0 = adr2 ∧ adr = adr4 ∧ err = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 7:
p_os < pmaxino, pmaxino ≤ jmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, pmaxino ≠ 0, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), inv-journal(nx, gstore, gstore0, jro), ri-inj(fi), ri-inj(fi0), gstore1 = gstore, nx0 = nx, jro0 = jro ⊦ ⟪gjournal_journal_addn#(ndx, jvalid0, fi, fi0, gstore0, pmaxino, p_os; ax, jvalid, jmaxino0, jro, gstore, nx, jvalid1; err)⟫ ( (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ ( err = ESUCCESS → # ax = # ndx ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx, gstore, jro) ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0)[ax, ndx] ∧ new(ax, nodes(gstore1 ↓, jro0))) ∧ (err ≠ ESUCCESS → abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0)))
Proof step 8:
jvalid2 ↔ jvalid1, fi2 = ri, fi3 = fi1, fs = nodes(gstore ↓, jro0), gstore = gstore, gstore2 = gstore0, gstore3 = gstore, jmaxino2 = jmaxino1, jro0 = jro0, jro2 = jro0, log = abs-log(nx, gstore ↓), ndx0 = nd3 ' + nd0 ' + nd2 ', nx = nx, nx1 = nx, p_os0 = p_os, pmaxino0 = pmaxino, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino1, p_os < pmaxino, ri.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), inv-journal(nx, gstore, gstore0, jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), node-cons(nd3.key, nd3), node-cons(nd0.key, nd0), node-cons(nd2.key, nd2), refsize-cons(gstore, range ri), refsize-cons(gstore0, range fi1), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino1, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ [gjournal_journal_addn#(nd3 ' + nd0 ' + nd2 ', jvalid1, ri, fi1, gstore0, pmaxino, p_os; ax, jvalid3, jmaxino, jro0, gstore, nx, jvalid4; err)] ( (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi2.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi2) ∧ inv-journal(nx, gstore, gstore2, jro0) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore3 ⊆ dom gstore ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore3 = ∅ ∧ ( err = ESUCCESS → # ax = # ndx0 ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx0, gstore, jro0) ∧ abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) + ax ∧ nodes(gstore ↓, jro0) = nodes(gstore3 ↓, jro2)[ax, ndx0] ∧ new(ax, nodes(gstore3 ↓, jro2))) ∧ (err ≠ ESUCCESS → abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) ∧ nodes(gstore ↓, jro0) = nodes(gstore3 ↓, jro2)) → ⟪adr1 := adr5; adr0 := adr2; adr := adr4; if err = ESUCCESS then {adr1 := ax[0]; adr0 := ax[1]; adr := ax[2]}⟫ ⟨aubifs_core_journal_add3#(nd3, nd0, nd2, ri, fi1, jro1.keys, p_os.keys; adr5, adr2, adr4, fs, log; jvalid5, err0)⟩ (log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid5 → jvalid4) ∧ adr1 = adr5 ∧ adr0 = adr2 ∧ adr = adr4 ∧ err = err0)), jmaxino1 = 0, pmaxino = 0, dups(nx)

Rule argument

spec: gjournal-asm name: inv-addn seq: p_os < pmaxino, pmaxino ≤ jmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, pmaxino ≠ 0, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), inv-journal(nx, gstore, gstore0, jro), ri-inj(fi), ri-inj(fi0), gstore1 = gstore, nx0 = nx, jro0 = jro ⊦ ⟪gjournal_journal_addn# (ndx, jvalid0, fi, fi0, gstore0, pmaxino, p_os ; ax, jvalid, jmaxino0, jro, gstore, nx, jvalid1 ; err)⟫ ( (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ ( err = ESUCCESS → # ax = # ndx ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx, gstore, jro) ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0)[ax, ndx] ∧ new(ax, nodes(gstore1 ↓, jro0))) ∧ ( err ≠ ESUCCESS → abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0))) subst: [p_os, pmaxino, gstore0, fi0, fi, jvalid0, ndx, jvalid1, nx, gstore, jro, jmaxino0, jvalid, ax, err, jmaxino, gstore1, nx0, jro0] → [p_os, pmaxino, gstore0, fi1, ri, jvalid1, nd3 ' + nd0 ' + nd2 ', jvalid4, nx, gstore, jro0, jmaxino, jvalid3, ax, err, jmaxino1, gstore, nx, jro0] flags: <all paths>

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) → ri-inj(ri); (ss)