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Proof step 10 from proof refine-add5 (previous step)

fs = nodes(gstore ↓, jro0), gstore3 = gstore, jro2 = jro0, log = abs-log(nx, gstore ↓), nx1 = nx, 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), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), node-cons(nd7.key, nd7), node-cons(nd6.key, nd6), node-cons(nd1.key, nd1), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), 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) ⊦ ∀ ax, jvalid3, jmaxino, jro0, gstore, nx, jvalid4, err. (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ ri.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range ri) ∧ inv(gstore \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro0 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore3 ⊆ dom gstore ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore3 = ∅ ∧ ( err = ESUCCESS → # ax = 5 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd7 ' + nd6 ' + nd1 ' + nd5 ' + nd4 ', gstore, jro0) ∧ abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) + ax ∧ nodes(gstore ↓, jro0) = nodes(gstore3 ↓, jro2)[ax, nd7 ' + nd6 ' + nd1 ' + nd5 ' + nd4 '] ∧ new(ax, nodes(gstore3 ↓, jro2))) ∧ (err ≠ ESUCCESS → abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) ∧ nodes(gstore ↓, jro0) = nodes(gstore3 ↓, jro2)) → ⟪adr13 := adr9; adr12 := adr10; adr1 := adr4; adr0 := adr6; adr := adr8; if err = ESUCCESS then {adr13 := ax[0]; adr12 := ax[1]; adr1 := ax[2]; adr0 := ax[3]; adr := ax[4]}⟫ ⟨aubifs_core_journal_add5#(nd7, nd6, nd1, nd5, nd4, ri, fi1, jro1.keys, p_os.keys; adr9, adr10, adr4, adr6, adr8, fs, log; jvalid5, err0)⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid5 → jvalid4) ∧ adr13 = adr9 ∧ adr12 = adr10 ∧ adr1 = adr4 ∧ adr0 = adr6 ∧ adr = adr8 ∧ err = err0), jmaxino1 = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro, 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(gstore1 \ jro), inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), node-cons(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd1.key, nd1), node-cons(nd6.key, nd6), node-cons(nd7.key, nd7), refsize-cons(gstore1, range ri), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino1, dom gstore ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ri.lebs ⊆ dom gstore1, ¬ dups(nx), ¬ dups(nx0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), err = ESUCCESS → # ax = 5 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd7 ' + nd6 ' + nd1 ' + nd5 ' + nd4 ', gstore1, jro) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[ax, nd7 ' + nd6 ' + nd1 ' + nd5 ' + nd4 '] ∧ new(ax, nodes(gstore ↓, jro0)), err ≠ ESUCCESS → abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) ∧ nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪adr13 := adr9; adr12 := adr10; adr1 := adr4; adr0 := adr6; adr := adr8; if err = ESUCCESS then {adr13 := ax[0]; adr12 := ax[1]; adr1 := ax[2]; adr0 := ax[3]; adr := ax[4]}⟫ ⟨aubifs_core_journal_add5#(nd7, nd6, nd1, nd5, nd4, ri, fi1, jro1.keys, p_os.keys; adr9, adr10, adr4, adr6, adr8, fs, log; jvalid5, err0)⟩ ( log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid5 → jvalid) ∧ adr13 = adr9 ∧ adr12 = adr10 ∧ adr1 = adr4 ∧ adr0 = adr6 ∧ adr = adr8 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: sub-trans: ⊦ ns ⊆ ns0 ∧ ns0 ⊆ ns1 → ns ⊆ ns1; (forward) from specification set-basic[nat-set]