[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 57 from proof refine-check-commit (previous step)

p_os.keys = p_os0.keys, abs-log(nx0, gstore0 ↓) = abs-log(nx, gstore2 ↓), nodes(gstore0 ↓, jro) = nodes(gstore2 ↓, jro2), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro2 = ∅, dom remove-refsize0(gstore2) ∩ jro2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro2, jmaxino ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os0.keys.inodes?, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, fi1.inos < pmaxino, inv(gstore1), inv(gstore2 \ jro2), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro2)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro2)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ⌊err1⌋ , ¬ dups(nx), jvalid4 → jvalid3, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro2), jvalid2 → jvalid0 ⊦ ∃ as. as ∩ range ri = ∅ ∧ ⟨fi := ri, fo := jro1.keys, fs := nodes(gstore2 ↓, jro2) \ as, log := [], err := ESUCCESS; jvalid5 := true⟩ (p_os0.keys = fo ∧ fi1 = fi ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro2) ∧ (jvalid5 → jvalid3) ∧ err1 = err), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; jvalid5 := ?⟩ ((jvalid5 → jvalid3) ∧ err1 = err)

User applied rule exists right

And obtained the following new goals

Proof step 58:
p_os.keys = p_os0.keys, abs-log(nx0, gstore0 ↓) = abs-log(nx, gstore2 ↓), nodes(gstore0 ↓, jro) = nodes(gstore2 ↓, jro2), remove-refsize0(gstore1) = gstore1, dom remove-refsize0(gstore2) ∩ jro2 = ∅, elems nx ∩ jro2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro2, p_os0.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, inv(gstore2 \ jro2), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro2)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-cons(ri, nodes(gstore2 ↓, jro2)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ⌊err1⌋ , jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro2), jvalid4 → jvalid3 ⊦ ⌊err1⌋ ∧ ⟨err := err1; jvalid5 := ?⟩ ((jvalid5 → jvalid3) ∧ err1 = err), ∃ as. as ∩ range ri = ∅ ∧ ⟨fi := ri, fo := jro1.keys, fs := nodes(gstore2 ↓, jro2) \ as, log := [], err := ESUCCESS; jvalid5 := true⟩ (p_os0.keys = fo ∧ fi1 = fi ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro2) ∧ (jvalid5 → jvalid3) ∧ err1 = err), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 2 terms: err1 abort: F discard: T computed: T

Additional information

Used terms: err1