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Proof step 53 from proof refine-commit (previous step)

remove-refsize0(gstore1) = gstore1, dom remove-refsize0(gstore2) ∩ jro3 = ∅, elems nx ∩ jro3 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro3, jmaxino ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro3), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro3)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro3)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro3) ⊦ ∃ as. as ∩ range ri = ∅ ∧ ⟨fi1 := ri, fo := jro1.keys, fs := nodes(gstore2 ↓, jro3) \ as, log := [], err := ESUCCESS; jvalid := true⟩ (jro1.keys = fo ∧ ri = fi1 ∧ log = [] ∧ fs = nodes(remove-refsize0(gstore2 ↓), ∅) ∧ ESUCCESS = err)

User applied rule exists right

And obtained the following new goals

Proof step 54:
remove-refsize0(gstore1) = gstore1, elems nx ∩ jro3 = ∅, dom remove-refsize0(gstore2) ∩ jro3 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro3, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore1), inv(gstore2 \ jro3), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro3)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-cons(ri, nodes(gstore2 ↓, jro3)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro3), jvalid2 → jvalid0 ⊦ refsize0-addresses((gstore2 \ jro3)↓) ∩ range ri = ∅ ∧ ⟨fi1 := ri, fo := jro1.keys, fs := nodes(gstore2 ↓, jro3) \ refsize0-addresses((gstore2 \ jro3)↓), log := [], err := ESUCCESS; jvalid := true⟩ (jro1.keys = fo ∧ ri = fi1 ∧ log = [] ∧ fs = nodes(remove-refsize0(gstore2 ↓), ∅) ∧ ESUCCESS = err), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1 terms: refsize0-addresses((gstore2 \ jro3)↓) abort: F discard: T computed: F

Additional information

Used terms: refsize0-addresses((gstore2 \ jro3)↓)