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Proof step 175 from proof inv-gc-copy (previous step)

abs-log(nx1, gstore2 ↓) = [], ax0 = [], dom gstore1 = dom gstore3 ∪ jro, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0), nx = [], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino3, p_os < pmaxino, jro2 < jmaxino3, fi2.inos < jmaxino0, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro0), key-cons(ndx0), key-cons(ndx1), refsize-cons(gstore3, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), ndx0.flashsize ≤ LEB_SIZE, pmaxino ≤ jmaxino0, pmaxino ≤ jmaxino3, jmaxino3 ≤ jmaxino0, dom gstore2 ⊆ dom gstore3, fi2.lebs ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), ndx0.keys.toSet ⊆ dom fi2, ndx1.keys.toSet ⊆ dom fi2, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), ∃ nd, ndx1. ndx0 = nd ' + ndx1, ndx1 = [] ∨ LEB_SIZE < ndx0.flashsize + ndx1.head.flashsize ⊦ ⟪gjournal_journal_addn#(ndx0, jvalid2, fi2, fi1, gstore1, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore3, nx, jvalid0; err); ndx2 := ndx0 + ndx1; fi := fi2; if err = ESUCCESS then gjournal_gc_update_index#(jvalid1, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; ax0, ndx0, jmaxino0, fi, gstore3)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx. ndx2 = ndx + ndx1) ∧ jmaxino3 ≤ jmaxino0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro)) ∧ fi.inos < jmaxino0 ∧ fi.lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi) ∧ inv(gstore3 \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore3 ∪ jro ∧ ri-inj(fi) ∧ ndx1.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore3 ↓, jro) ∧ dom gstore2 ⊆ dom gstore3 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅ ∧ (∃ ndx, ndx0. ndx2 = ndx + ndx0 ∧ (err = ESUCCESS → ndx0 = ndx1) ∧ new(abs-log(nx, gstore3 ↓), nodes(gstore2 ↓, jro0)) ∧ ¬ dups(abs-log(nx, gstore3 ↓)) ∧ # abs-log(nx, gstore3 ↓) = # ndx ∧ fi = fi2[ndx.keys, abs-log(nx, gstore3 ↓)] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[abs-log(nx, gstore3 ↓), ndx]) ∧ (err = ESUCCESS ⊃ # ndx1;0) < # ndx2), ndx0 + ndx1 = [], jmaxino3 = 0, pmaxino = 0, dups(nx1), dups(ndx0.keys + ndx1.keys), dups(ndx0.keys), dups(ndx1.keys)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 176:
abs-log(nx1, gstore2 ↓) = [], ax0 = [], dom gstore1 = dom gstore3 ∪ jro, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0), nx = [], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jmaxino3 ≠ 0, pmaxino ≠ 0, fi2.inos < jmaxino0, jro2 < jmaxino3, p_os < pmaxino, fi2.inos < jmaxino3, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore3 \ jro), key-cons(ndx1), key-cons(nd.key, nd), key-cons(ndx), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), nd.key ∈ fi2, jmaxino3 ≤ jmaxino0, pmaxino ≤ jmaxino3, pmaxino ≤ jmaxino0, nd.flashsize + ndx.flashsize ≤ LEB_SIZE, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ndx1.keys.toSet ⊆ dom fi2, ndx.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi2.lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, ¬ dups(nx1), ¬ dups(ndx.keys + ndx1.keys), ¬ dups(ndx.keys), ¬ dups(ndx1.keys), ¬ nd.key ∈ ndx.keys, ¬ nd.key ∈ ndx1.keys, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), ndx1 = [] ∨ LEB_SIZE < (nd.flashsize + ndx.flashsize) + ndx1.head.flashsize ⊦ ⟪gjournal_journal_addn#(nd ' + ndx, jvalid2, fi2, fi1, gstore1, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore3, nx, jvalid0; err); ndx2 := (nd ' + ndx) + ndx1; fi := fi2; if err = ESUCCESS then {ndx0 := nd ' + ndx; gjournal_gc_update_index#(jvalid1, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; ax0, ndx0, jmaxino0, fi, gstore3)}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx. ndx2 = ndx + ndx1) ∧ jmaxino3 ≤ jmaxino0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro)) ∧ fi.inos < jmaxino0 ∧ fi.lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi) ∧ inv(gstore3 \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore3 ∪ jro ∧ ri-inj(fi) ∧ ndx1.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore3 ↓, jro) ∧ dom gstore2 ⊆ dom gstore3 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅ ∧ (∃ ndx, ndx0. ndx2 = ndx + ndx0 ∧ (err = ESUCCESS → ndx0 = ndx1) ∧ new(abs-log(nx, gstore3 ↓), nodes(gstore2 ↓, jro0)) ∧ ¬ dups(abs-log(nx, gstore3 ↓)) ∧ # abs-log(nx, gstore3 ↓) = # ndx ∧ fi = fi2[ndx.keys, abs-log(nx, gstore3 ↓)] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[abs-log(nx, gstore3 ↓), ndx]) ∧ (err = ESUCCESS ⊃ # ndx1;0) < # ndx2)

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(kx + kx0) → ¬ dups(kx) ∧ ¬ dups(kx0); (forward) from specification list-dup[key-list-set]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ key ∈ kx + kx0 ↔ key ∈ kx ∨ key ∈ kx0; (s)% ⊦ dups(key ' + kx) ↔ dups(kx) ∨ key ∈ kx; (ws)% ⊦ key-cons(nd ' + ndx) ↔ ¬ ¬(key-cons(nd.key, nd) ∧ key-cons(ndx)); (s)% ⊦ (nd ' + ndx).flashsize = nd.flashsize + ndx.flashsize; (s)% ⊦ key ∈ dom ri ↔ key ∈ ri; (s)% ⊦ ks ++ key ⊆ ks0 ↔ ks ⊆ ks0 ∧ key ∈ ks0; (ws)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]%unc: ⊦ ks ∪ ks0 = ks0 ∪ ks; from specification set-union[node-index]%una: ⊦ (ks ∪ ks0) ∪ ks1 = ks ∪ ks0 ∪ ks1; from specification set-union[node-index]% ⊦ ks ∪ ∅ = ks; (s)% ⊦ (ks ++ key) ∪ ks0 = (ks ∪ ks0) ++ key; (s)% ⊦ key '.toSet = ∅ ++ key; (s)% ⊦ (kx + kx0).toSet = kx.toSet ∪ kx0.toSet; (s)% ⊦ key + kx = key ' + kx; (s)% ⊦ (nd ' + ndx).keys = nd.key + ndx.keys; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ nd ' + ndx ≠ []; (s)