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Proof step 166 from proof inv-gc-copy (previous step)

abs-log(nx1, gstore2 ↓) = [], dom gstore1 = dom gstore3 ∪ jro, ndx = [], ndx2 = ndx4, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0), remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, fi2.inos < jmaxino0, jro2 < jmaxino3, p_os < pmaxino, fi2.inos < jmaxino3, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore3 \ jro), key-cons(ndx4), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), jmaxino3 ≤ jmaxino0, pmaxino ≤ jmaxino3, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ndx4.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi2.lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0) ⊦ ∀ ndx4, ndx. ndx2 = ndx + ndx4 ∧ ndx.flashsize ≤ LEB_SIZE ∧ (ndx4 = [] ∨ LEB_SIZE < ndx.flashsize + ndx4.head.flashsize) → ⟪nx := []; fi := fi2; if ndx = [] then err := EINVAL else {ax0 := []; gjournal_journal_addn#(ndx, jvalid2, fi, fi1, gstore1, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore3, nx, jvalid0; err); if err = ESUCCESS then gjournal_gc_update_index#(jvalid1, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; ax0, ndx, jmaxino0, fi, gstore3)}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx. ndx2 = ndx + ndx4) ∧ 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) ∧ ndx4.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore3 ↓, jro) ∧ dom gstore2 ⊆ dom gstore3 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅ ∧ (∃ ndx, ndx1. ndx2 = ndx + ndx1 ∧ (err = ESUCCESS → ndx1 = ndx4) ∧ 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 ⊃ # ndx4;0) < # ndx2), jmaxino3 = 0, ndx4 = [], pmaxino = 0, dups(ndx4.keys), dups(nx1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 167:
abs-log(nx1, gstore2 ↓) = [], dom gstore1 = dom gstore3 ∪ jro, ndx2 = ndx0 + ndx1, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0), remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, ndx0 + ndx1 ≠ [], jmaxino3 ≠ 0, pmaxino ≠ 0, 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, ¬ dups(nx1), ¬ dups(ndx0.keys + ndx1.keys), ¬ dups(ndx0.keys), ¬ dups(ndx1.keys), jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), ndx1 = [] ∨ LEB_SIZE < ndx0.flashsize + ndx1.head.flashsize ⊦ ⟪nx := []; fi := fi2; if ndx0 = [] then err := EINVAL else {ax0 := []; gjournal_journal_addn#(ndx0, jvalid2, fi, fi1, gstore1, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore3, nx, jvalid0; err); 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)

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(kx + kx0) → ¬ dups(kx) ∧ ¬ dups(kx0); (forward) from specification list-dup[key-list-set]% ⊦ key-cons(ndx0 + ndx1) ↔ key-cons(ndx0) ∧ key-cons(ndx1); (s)%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 ∪ ks0 ⊆ ks1 ↔ ks ⊆ ks1 ∧ ks0 ⊆ ks1; (ws)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ (kx + kx0).toSet = kx.toSet ∪ kx0.toSet; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ (ndx0 + ndx1).keys = ndx0.keys + ndx1.keys; (s)