[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 38 from proof inv-io-save (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), istore1 = istore3, pstate = index(m), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore2) = istore2, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, ((btree(rp, r, adr1, height, dirty, ri, nodes(istore3), as, alladrs, ok) * P))(zh), n < save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, btree-sub-clean(r, m0, zh), inv(gstore2 \ ginval2), inv(gstore1), inv(istore3), inv(istore2), refsize-cons(istore3, as0 ∪ as), r ∈ zh, m ∈ istore3, n ≤ LEB_SIZE, as0 ⊆ dom nodes(istore3), alladrs ⊆ dom nodes(istore3), as ⊆ alladrs, as ⊆ dom nodes(istore3), istore2 ⊑ istore3, ¬ dups(nx), ¬ adr1 ∈ as, height = 0 → as = ∅ ⊦ ⟪apersistence_allocate_ind#(adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, true; istore3, pstate; err0); adr := adr1; syn := true; if err0 = ESUCCESS then {apersistence_add_ind# (save(mkznode(r0, zbrar, boolvar, true, m0)), adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval; adr, istore3, pstate, syn; err0); if err0 = ESUCCESS then let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore3, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino + adr.size, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; istore3)}}; if err0 = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore3, as0 ∪ (err0 = ESUCCESS ⊃ as ++ adr;as)) ∧ inv(istore3) ∧ istore2 ⊑ istore3 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore3) ∧ (pstate = unbuffered → syn) ∧ istore1 ⊑ istore3 ∧ r ∈ zh ∧ (err0 = ESUCCESS → ¬ adr ∈ as) ∧ dom nodes(istore3) = dom nodes(istore1) ∪ (err0 = ESUCCESS ⊃ ∅ ++ adr;∅) ∧ (err0 = ESUCCESS → ¬ adr ∈ istore1) ∧ (( btree (rp, r, (err0 = ESUCCESS ⊃ adr;adr1), height, err0 ≠ ESUCCESS, ri, nodes(istore3), (err0 = ESUCCESS ⊃ as ++ adr;as), (err0 = ESUCCESS ⊃ (alladrs -- adr1) ++ adr;alladrs), ok) * P) )(zh) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → pstate.index? ∧ ¬ zh[r].dirty))

User applied rule insert program lemma

And obtained the following new goals

Proof step 39:
inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), syn ⊦ ⟪apersistence_allocate_ind#(adr, istore0, ginval, gstore, gstore0, nx, maxino, ginval0, syn; istore, pstate; err)⟫ (inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn))
Proof step 40:
syn0 ↔ true, zh[r] = mkznode(r0, zbrar, boolvar, true, m0), adr2 = adr0, ginval1 = ginval2, ginval3 = ginval, gstore3 = gstore2, gstore4 = gstore1, istore1 = istore3, istore4 = istore2, maxino1 = maxino0, nx0 = nx, pstate = index(m), remove-refsize0(istore2) = istore2, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, ((btree(rp, r, adr1, height, dirty, ri, nodes(istore3), as, alladrs, ok) * P))(zh), n < save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, btree-sub-clean(r, m0, zh), inv(istore2), inv(istore3), inv(gstore1), inv(gstore2 \ ginval2), inv-index(istore3, istore2), inv-journal(nx, gstore2, gstore1, ginval2), inv-state(pstate, nx, gstore2, istore3, true), refsize-cons(istore3, as0 ∪ as), m ∈ istore3, r ∈ zh, n ≤ LEB_SIZE, as ⊆ dom nodes(istore3), as ⊆ alladrs, alladrs ⊆ dom nodes(istore3), as0 ⊆ dom nodes(istore3), istore2 ⊑ istore3, height = 0 → as = ∅ ⊦ [apersistence_allocate_ind#(adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, true; istore3, pstate; err0)] ( inv-index(istore3, istore4) ∧ inv-state(pstate, nx0, gstore3, istore3, syn0) → ⟪adr := adr1; syn := true; if err0 = ESUCCESS then {apersistence_add_ind# (save(mkznode(r0, zbrar, boolvar, true, m0)), adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval ; adr, istore3, pstate, syn ; err0); if err0 = ESUCCESS then let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore3, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino + adr.size, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; istore3)}}; if err0 = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore3, as0 ∪ (err0 = ESUCCESS ⊃ as ++ adr;as)) ∧ inv(istore3) ∧ istore2 ⊑ istore3 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore3) ∧ (pstate = unbuffered → syn) ∧ istore1 ⊑ istore3 ∧ r ∈ zh ∧ (err0 = ESUCCESS → ¬ adr ∈ as) ∧ dom nodes(istore3) = dom nodes(istore1) ∪ (err0 = ESUCCESS ⊃ ∅ ++ adr;∅) ∧ (err0 = ESUCCESS → ¬ adr ∈ istore1) ∧ (( btree (rp, r, (err0 = ESUCCESS ⊃ adr;adr1), height, err0 ≠ ESUCCESS, ri, nodes(istore3), (err0 = ESUCCESS ⊃ as ++ adr;as), (err0 = ESUCCESS ⊃ (alladrs -- adr1) ++ adr;alladrs), ok) * P) )(zh) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → pstate.index? ∧ ¬ zh[r].dirty))), dups(nx), adr1 ∈ as

Rule argument

spec: apersistence-asm name: inv-allocate-ind seq: inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), syn ⊦ ⟪apersistence_allocate_ind# (adr, istore0, ginval, gstore, gstore0, nx, maxino, ginval0, syn ; istore, pstate ; err)⟫ ( inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn)) subst: [syn, ginval0, maxino, nx, gstore0, gstore, ginval, istore0, adr, pstate, istore, err] → [true, ginval, maxino0, nx, gstore1, gstore2, ginval2, istore2, adr0, pstate, istore3, err0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)% ⊦ ¬ index(m).journal?; (s)% ⊦ index(m).index?; (s)% ⊦ index(m).lnum = m; (s)