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Proof step 6 from proof inv-gc-copy (previous step)

jvalid2 ↔ jvalid4, jvalid1 ↔ jvalid, jvalid0 ↔ jvalid3, err = ESUCCESS, fi1 = fi, gstore1 = gstore, jmaxino0 = jmaxino, jmaxino2 = jmaxino, jro = jro0, jro1 = jro0, ndx2 = ndx, ndx3 = ndx, nx0 = nx, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, jro2 < jmaxino, inv(gstore0), inv(gstore \ jro0), key-cons(ndx), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-inj(fi0), ri-inj(fi), pmaxino ≤ jmaxino, range fi ⊆ dom nodes(gstore ↓, jro0), ndx.keys.toSet ⊆ dom fi, fi0.lebs ⊆ dom gstore0, fi.lebs ⊆ dom gstore, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪while err = ESUCCESS ∧ ndx2 ≠ [] do {/* (inv-gc-copy : invariant (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx0. ndx2` = ndx0 + ndx2) ∧ jmaxino0 ≥ jmaxino0` ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.inos < jmaxino0 ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro) ∧ ri-inj(fi) ∧ ndx2.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore ↓, jro) ∧ dom gstore` ⊆ dom gstore ∧ (nx.toSet \ nx`.toSet) ∩ dom gstore` = ∅ ∧ (∃ ax, ndx0, ndx1. ndx2` = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = ndx2) ∧ new(ax, nodes(gstore` ↓, jro`)) ∧ ¬ dups(ax) ∧ # ax = # ndx0 ∧ fi = (fi`)[ndx0.keys, ax] ∧ nodes(gstore ↓, jro) = nodes(gstore` ↓, jro`)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx`, gstore` ↓) + ax) wfbound (err = ESUCCESS ⊃ # ndx2;0)) */; let jmaxino = 0, jvalid = ? in {index_is_log_empty#(fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; jvalid); if ¬ jvalid then {index_get_block_free_size#(fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; jmaxino); if jmaxino < ndx2.head.flashsize then jmaxino := 0}; let ndx = [], ax0 = [], n = ? in {index_get_leb_size(fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; n); gjournal_split_nodes#(n - jmaxino; ndx2, ndx); if ndx = [] then err := EINVAL else {gjournal_journal_addn#(ndx, jvalid2, fi, fi0, gstore0, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore, nx, jvalid0; err); if err = ESUCCESS then gjournal_gc_update_index#(jvalid1, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid0; ax0, ndx, jmaxino0, fi, gstore)}}}}⟫ ( jro2 < jmaxino0 ∧ pmaxino ≤ jmaxino0 ∧ fi.inos < jmaxino0 ∧ jmaxino0 ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro ∧ ri-inj(fi) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ jmaxino2 ≤ jmaxino0 ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ (∃ ax, ndx0, ndx1. ndx3 = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = []) ∧ new(ax, nodes(gstore1 ↓, jro1)) ∧ # ax = # ndx0 ∧ ¬ dups(ax) ∧ fi = fi1[ndx0.keys, ax] ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro1)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax)), jmaxino = 0, pmaxino = 0, dups(ndx.keys), dups(nx)

Heuristic annotation applied rule annotation right

And obtained the following new goals

Rule argument

rule: invariant right arg: bound: (err = ESUCCESS ⊃ # ndx2;0) inv: (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx0. ndx2` = ndx0 + ndx2) ∧ jmaxino0 ≥ jmaxino0` ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.inos < jmaxino0 ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro) ∧ ri-inj(fi) ∧ ndx2.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore ↓, jro) ∧ dom gstore` ⊆ dom gstore ∧ (nx.toSet \ nx`.toSet) ∩ dom gstore` = ∅ ∧ (∃ ax, ndx0, ndx1. ndx2` = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = ndx2) ∧ new(ax, nodes(gstore` ↓, jro`)) ∧ ¬ dups(ax) ∧ # ax = # ndx0 ∧ fi = (fi`)[ndx0.keys, ax] ∧ nodes(gstore ↓, jro) = nodes(gstore` ↓, jro`)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx`, gstore` ↓) + ax) fmapos: right 1 pos: right 1

Additional information

Used simplifier rules: ⊦ ndx = ndx0 + ndx ↔ ndx0 = []; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ m; (s)%⊦ 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)% ⊦ ns ⊆ ns; (s)% ⊦ ns \ ns = ∅; (s)% ⊦ ns ∩ ∅ = ∅; (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]% ⊦ # [] = 0; (s)% ⊦ # ax = 0 ↔ ax = []; (s)% ⊦ [].keys = []; (s)% ⊦ ri[[], []] = ri; (s)% ⊦ fs[[], []] = fs; (s)% ⊦ ax + [] = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ [] + ndx = ndx; (s)% ⊦ new([], fs); (s)% ⊦ ¬ dups([]); (s) Used formulas: (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx0. ndx2` = ndx0 + ndx2) ∧ jmaxino0 ≥ jmaxino0` ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.inos < jmaxino0 ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro) ∧ ri-inj(fi) ∧ ndx2.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore ↓, jro) ∧ dom gstore` ⊆ dom gstore ∧ (nx.toSet \ nx`.toSet) ∩ dom gstore` = ∅ ∧ (∃ ax, ndx0, ndx1. ndx2` = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = ndx2) ∧ new(ax, nodes(gstore` ↓, jro`)) ∧ ¬ dups(ax) ∧ # ax = # ndx0 ∧ fi = (fi`)[ndx0.keys, ax] ∧ nodes(gstore ↓, jro) = nodes(gstore` ↓, jro`)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx`, gstore` ↓) + ax), (err = ESUCCESS ⊃ # ndx2;0) = (err = ESUCCESS ⊃ # ndx2;0)