[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,

Theorem inv-io-save

adr0 = adr1, r ∈ zh, zh[r].dirty, btree-sub-clean(r, zh[r].usedsize, zh), ((btree(rp, r, adr0, height, dirty, ri, nodes(istore), as, alladrs, ok) * P))(zh), as0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), refsize-cons(istore, as0 ∪ as), inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), pstate.index?, istore1 = istore ⊦ ⟪btree_io_save#(r, adr, istore0, ginval, gstore, gstore0, nx, maxino, ginval0; adr1, zh, istore, pstate, syn; err)⟫ ( refsize-cons(istore, as0 ∪ (err = ESUCCESS ⊃ as ++ adr1;as)) ∧ inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn) ∧ istore1 ⊑ istore ∧ r ∈ zh ∧ (err = ESUCCESS → ¬ adr1 ∈ as) ∧ (∃ as0, alladrs0. as0 = (err = ESUCCESS ⊃ as ++ adr1;as) ∧ alladrs0 = (err = ESUCCESS ⊃ (alladrs -- adr0) ++ adr1;alladrs) ∧ dom nodes(istore) = dom nodes(istore1) ∪ (err = ESUCCESS ⊃ {adr1} ;∅) ∧ (err = ESUCCESS → ¬ adr1 ∈ istore1) ∧ ((btree(rp, r, (err = ESUCCESS ⊃ adr1;adr0), height, err ≠ ESUCCESS, ri, nodes(istore), as0, alladrs0, ok) * P))(zh)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → pstate.index? ∧ ¬ zh[r].dirty))

View the proof

Infos about the proof