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Proof step 118 from proof refine-commit (previous step)

p_os.keys = fo, jvalid ↔ jvalid0, fi = fi2, fi0 = ri, fi2 = fi1, fs = nodes(gstore2 ↓, jro0), gstore = gstore1, gstore0 = gstore2, jro1 = jro, log = abs-log(nx, gstore2 ↓), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv(gstore1), inv(gstore2 \ jro0), 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), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 → jvalid0 ⊦ jmaxino = 0, pmaxino = 0, dups(nx), dom remove-refsize0(gstore0) ∩ jro0 = ∅ ∧ fi0.lebs ⊆ dom remove-refsize0(gstore0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 119:
remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv(gstore1), inv(gstore2 \ jro0), 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), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 → jvalid0 ⊦ #(dom remove-refsize0(gstore2) ∩ jro0) = 0, jmaxino = 0, pmaxino = 0, dom remove-refsize0(gstore2) ∩ jro0 = ∅, dups(nx)

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # ns ≠ 0 → ns ≠ ∅; (forward) from specification set-basic[nat-set]%size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%⊦ ri-cons(ri, nodes(gstore ↓, ginval)) ∧ refsize-cons(gstore, range ri) ∧ inv(gstore \ ginval) → ri.lebs ⊆ dom remove-refsize0(gstore); (s)