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Proof step 100 from proof refine-gc (previous step)

# lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), fi = ri, fs = nodes(gstore2 ↓, jro0), log = abs-log(nx, gstore2 ↓), ndx = nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)], remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, ri.inos < jmaxino, jro1 < jmaxino, p_os < pmaxino, fi1.inos < pmaxino, inv(groupblock(gndx0, lax, m0)), inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri), ri-inj(fi1), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ jmaxino = 0, m0 = 0, pmaxino = 0, dups(nx), n1 ∈ nx, n1 ∈ jro0, jro1 < jmaxino ∧ p_os < pmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ fi1.inos < pmaxino ∧ jmaxino ≠ 0 ∧ pmaxino ≠ 0 ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ fi1.lebs ⊆ dom gstore1 ∧ refsize-cons(gstore2, range fi) ∧ refsize-cons(gstore1, range fi1) ∧ inv-journal(nx, gstore2, gstore1, jro0) ∧ ri-inj(fi) ∧ ri-inj(fi1) ∧ ndx.keys.toSet ⊆ dom fi ∧ ¬ dups(ndx.keys) ∧ range fi ⊆ dom nodes(gstore2 ↓, jro0) ∧ key-cons(ndx) ∧ jmaxino = jmaxino ∧ gstore2 = gstore2 ∧ nx = nx ∧ ndx = ndx ∧ jro0 = jro0 ∧ fi = fi

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 101:
# lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, p_os < pmaxino, jro1 < jmaxino, ri.inos < jmaxino, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys), inv(gstore2 \ jro0), inv(gstore1), inv(groupblock(gndx0, lax, m0)), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(ri), n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid4 ⊦ jmaxino = 0, m0 = 0, pmaxino = 0, dups(nx), n1 ∈ jro0, n1 ∈ nx

Rule argument

Additional information

Used simplifier rules: ⊦ ri-cons(ri, fs) → key-cons(fs[referenced-adrs(ax, ri)]); (s)% ⊦ ri-cons(ri, fs) → range ri ⊆ dom fs; (ss)% ⊦ ri-cons(ri, fs) → fs[referenced-adrs(ax, ri)].keys.toSet ⊆ dom ri; (s)% ⊦ ri-cons(ri, fs) → ri-inj(ri); (ss)%⊦ 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)