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Proof step 229 from proof inv-io-save (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), istore4[m] = indexblock(indx, lax, m1), 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(istore4), as, alladrs, ok) * P))(zh), btree-sub-clean(r, m0, zh), inv(indexblock(indx, lax, m1)), inv (istore4 [m, indexblock(indx + save(mkznode(r0, zbrar, boolvar, true, m0)) ', lax + @(maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', m1) ]), inv(istore2), inv(istore4), inv(gstore1), inv(gstore2 \ ginval2), refsize-cons(istore4, as0 ∪ as), m ∈ istore4, r ∈ zh, n ≤ LEB_SIZE, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ n, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ LEB_SIZE, as ⊆ dom nodes(istore4), as ⊆ alladrs, alladrs ⊆ dom nodes(istore4), as0 ⊆ dom nodes(istore4), istore2 ⊑ istore4, istore2 ⊑ istore4 [m, indexblock(indx + save(mkznode(r0, zbrar, boolvar, true, m0)) ', lax + @(maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', m1) ], ¬ dups(nx), ¬ adr1 ∈ as, ¬ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ istore4, ¬ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ istore2, height = 0 → as = ∅ ⊦ ⟪apersistence_get_iblock_refsize# (index(m).lnum, adr0, istore4 [index(m).lnum, istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist:= ( istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist + @ (@(index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize).pos, @(index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize).size) ') ], istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, index(m), syn ; ; maxino); istore3 := istore4 [index(m).lnum, istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist:= ( istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist + @ (@(index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize).pos, @(index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize).size) ') ]; apersistence_set_iblock_refsize# (index(m).lnum, maxino + @(index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize).size, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, index(m), syn ; istore3); err := ESUCCESS; if err = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore3, as0 ∪ (err = ESUCCESS ⊃ as ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as)) ∧ inv(istore3) ∧ istore2 ⊑ istore3 ∧ m ∈ istore3 ∧ istore4 ⊑ istore3 ∧ r ∈ zh ∧ (err = ESUCCESS → ¬ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ as) ∧ dom nodes(istore3) = dom nodes(istore4) ∪ (err = ESUCCESS ⊃ ∅ ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);∅) ∧ (( btree (rp, r, (err = ESUCCESS ⊃ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);adr1), height, err ≠ ESUCCESS, ri, nodes(istore3), (err = ESUCCESS ⊃ as ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as), (err = ESUCCESS ⊃ (alladrs -- adr1) ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);alladrs), ok) * P) )(zh) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ¬ zh[r].dirty))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 230:
@(index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) = @(m2, m3, m4), istore4[m] = indexblock(indx, lax, m1), zh[r] = mkznode(r0, zbrar, boolvar, true, m0), 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(istore4), as, alladrs, ok) * P))(zh), btree-sub-clean(r, m0, zh), inv(gstore2 \ ginval2), inv(gstore1), inv(istore4), inv(istore2), inv (istore4 [m, indexblock(indx + save(mkznode(r0, zbrar, boolvar, true, m0)) ', lax + @(maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', m1) ]), inv(indexblock(indx, lax, m1)), refsize-cons(istore4, as0 ∪ as), r ∈ zh, m ∈ istore4, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ LEB_SIZE, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ n, n ≤ LEB_SIZE, as0 ⊆ dom nodes(istore4), alladrs ⊆ dom nodes(istore4), as ⊆ alladrs, as ⊆ dom nodes(istore4), istore2 ⊑ istore4 [m, indexblock(indx + save(mkznode(r0, zbrar, boolvar, true, m0)) ', lax + @(maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', m1) ], istore2 ⊑ istore4, height = 0 → as = ∅ ⊦ ⟪apersistence_get_iblock_refsize# (index(m).lnum, adr0, istore4 [index(m).lnum, istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist:= ( istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist + @(m3, m4) ') ], istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, index(m), syn ; ; maxino); istore3 := istore4 [index(m).lnum, istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist:= ( istore4 [index(m).lnum, istore4[index(m).lnum].indlist:= (istore4[index(m).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m).lnum ] .ladrlist + @(m3, m4) ') ]; apersistence_set_iblock_refsize# (index(m).lnum, maxino + m4, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, index(m), syn; istore3); err := ESUCCESS; if err = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore3, as0 ∪ (err = ESUCCESS ⊃ as ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as)) ∧ inv(istore3) ∧ istore2 ⊑ istore3 ∧ m ∈ istore3 ∧ istore4 ⊑ istore3 ∧ r ∈ zh ∧ (err = ESUCCESS → ¬ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ as) ∧ dom nodes(istore3) = dom nodes(istore4) ∪ (err = ESUCCESS ⊃ ∅ ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);∅) ∧ (( btree (rp, r, (err = ESUCCESS ⊃ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);adr1), height, err ≠ ESUCCESS, ri, nodes(istore3), (err = ESUCCESS ⊃ as ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as), (err = ESUCCESS ⊃ (alladrs -- adr1) ++ @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);alladrs), ok) * P) )(zh) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ¬ zh[r].dirty)), dups(nx), adr1 ∈ as, @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ istore4, @(m, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ istore2

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [@ (index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize), m2, m3, m4]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: @ (index(m).lnum, maxino1, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize), m2, m3, m4