[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 14 from proof initialization (previous step)

# avol = # lpt + m9, avol[0] = mapped(buf), avol[m5] = mapped(mkbuf(0)), avol[m4] = mapped(mkbuf(0)), subarray(avol, m9, # lpt) = fill(mkavolume(# lpt0), unmapped), disk-layout(mksb(adr1, m3, m4, m5, 0, m8, m9), # lpt), ebm-vol-inv(avol), is-encoded(lpt, lebs(avol, m8, lptlebs(# lpt, LEB_SIZE))), is-encoded(lpt0, lebs(avol, m8, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr1, m3, m4, m5, 0, m8, m9), buf), mapped-full?(avol, m8, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → 0 = logoff ⊦ ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ ( m6 = m3 ∧ adr2 = adr1 ∧ avol1 = subarray(avol, m9, # lpt) ∧ [] = plog ∧ is-encoded(lpt1, lebs(avol, m8, lptlebs(# lpt, LEB_SIZE))) ∧ ∅ = ns0 ∧ ESUCCESS = err0)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 15:
# avol0 = # lpt2 + m9, avol0[m4] = mapped(mkbuf(0)), avol0[m5] = mapped(mkbuf(0)), avol0[0] = mapped(buf), adr0 = adr1, m0 = m3, m1 = LEB_SIZE, m2 = # lpt0, subarray(avol0, m9, # lpt2) = fill(mkavolume(# lpt0), unmapped), disk-layout(mksb(adr1, m3, m4, m5, 0, m8, m9), # lpt2), ebm-vol-inv(avol0), is-encoded(mksb(adr1, m3, m4, m5, 0, m8, m9), buf), is-encoded(lpt0, lebs(avol0, m8, lptlebs(# lpt2, LEB_SIZE))), is-encoded(lpt2, lebs(avol0, m8, lptlebs(# lpt2, LEB_SIZE))), mapped-full?(avol0, m8, lptlebs(# lpt2, LEB_SIZE)), logoff ≠ LEB_SIZE → 0 = logoff ⊦ ⟨if # lpt0 = m2 ∧ m1 = LEB_SIZE then {fail_or_success#(; ; err); if err = ESUCCESS then {avol := fill(mkavolume(m2), unmapped); adr := adr0; m := m0; plog := []; lpt := lpt0; ns := ∅} else avol := ?, adr := ?, m := ?, plog := ?, lpt := ?, ns := ?} else abort⟩ ( m = m3 ∧ adr = adr1 ∧ avol = subarray(avol0, m9, # lpt2) ∧ [] = plog ∧ is-encoded(lpt, lebs(avol0, m8, lptlebs(# lpt2, LEB_SIZE))) ∧ ∅ = ns ∧ ESUCCESS = err)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_io_format# (VOLSIZE, SIZE, LPT, PROOTADR0, PMAXINO0 ; ; PROOTADR, PMAXINO, PLOG, PVOL, PLPT, PORPHANS, ERR ) {if # LPT = VOLSIZE ∧ SIZE = LEB_SIZE then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then {PVOL := fill(mkavolume(VOLSIZE), unmapped); PROOTADR := PROOTADR0; PMAXINO := PMAXINO0; PLOG := []; PLPT := LPT; PORPHANS := ∅} else PVOL := ?, PROOTADR := ?, PMAXINO := ?, PLOG := ?, PLPT := ?, PORPHANS := ?} else abort };