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Proof step 376 from proof refine-gc (previous step)

jvalid4 ↔ true, gstore2[n1] = groupblock(gndx, lax, 0), err = ESUCCESS, err = err0, fi = ri, fs = nodes(gstore2 ↓, jro0), log = abs-log(nx, gstore2 ↓), 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(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 → jvalid, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [index_deallocate_gnd#(n1, fi, fi1, gstore1, nx, pmaxino, p_os, jvalid4; jro0, gstore2; err)] ( fi.inos < jmaxino ∧ (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi) → ⟨aubifs_core_journal_gc#(fi1, jro1.keys, p_os.keys; ri, fs, log; jvalid5)⟩ (fi = ri ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid5 → jvalid4))), jmaxino = 0, pmaxino = 0, dups(nx), n1 ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 377:
gstore2[n1] = groupblock(gndx, lax, 0), fs = nodes(gstore2 ↓, jro0), log = abs-log(nx, gstore2 ↓), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, p_os < pmaxino, jro1 < jmaxino, ri.inos < jmaxino, inv(gstore2 \ jro0), inv(gstore1), 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, ¬ dups(nx), ¬ n1 ∈ nx, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid ⊦ [index_deallocate_gnd#(n1, ri, fi1, gstore1, nx, pmaxino, p_os, true; jro0, gstore2; err0)] ( (jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ ri.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range ri) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 → ⟨ri0 := ri; aubifs_core_journal_gc#(fi1, jro1.keys, p_os.keys; ri, fs, log; jvalid5)⟩ (ri0 = ri ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0)))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ⌊ESUCCESS⌋ ; (s)