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Proof step 166 from proof inv-io-save (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), istore = istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], 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), n0 < save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, btree-sub-clean(r, m0, zh), inv(gstore2 \ ginval2), inv(gstore1), inv(istore3), inv(istore2), inv(istore3[m1, indexblock([], [], 0)]), inv(istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)]), refsize-cons(istore3, as0 ∪ as), r ∈ zh, m ∈ istore3, n0 ≤ LEB_SIZE, as0 ⊆ dom nodes(istore3), alladrs ⊆ dom nodes(istore3), as ⊆ alladrs, as ⊆ dom nodes(istore3), istore2 ⊑ istore3, istore2 ⊑ istore3[m1, indexblock([], [], 0)], istore2 ⊑ istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], ¬ dups(nx), ¬ adr1 ∈ as, ¬ m1 ∈ istore3, height = 0 → as = ∅ ⊦ ⟪apersistence_set_iblock_refsize# (index(m1).lnum, istore3[m1, indexblock([], [], 0)] [index(m1).lnum, istore3[m1, indexblock([], [], 0)] [index(m1).lnum, istore3[m1, indexblock([], [], 0)][index(m1).lnum] .indlist:= (istore3[m1, indexblock([], [], 0)][index(m1).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m1).lnum ] .ladrlist:= ( istore3[m1, indexblock([], [], 0)] [index(m1).lnum, istore3[m1, indexblock([], [], 0)][index(m1).lnum] .indlist:= (istore3[m1, indexblock([], [], 0)][index(m1).lnum].indlist + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m1).lnum ] .ladrlist + @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ') ] [index(m1).lnum ] .ref-size + save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino2, ginval, index(m1), syn ; istore); err0 := ESUCCESS; if err0 = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore, as0 ∪ (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as)) ∧ inv(istore) ∧ istore2 ⊑ istore ∧ m1 ∈ istore ∧ istore3 ⊑ istore ∧ r ∈ zh ∧ (err0 = ESUCCESS → ¬ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ as) ∧ dom nodes(istore) = dom nodes(istore3) ∪ (err0 = ESUCCESS ⊃ ∅ ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);∅) ∧ (( btree (rp, r, (err0 = ESUCCESS ⊃ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);adr1), height, err0 ≠ ESUCCESS, ri, nodes(istore), (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as), (err0 = ESUCCESS ⊃ (alladrs -- adr1) ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);alladrs), ok) * P) )(zh) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → ¬ zh[r].dirty))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 167:
zh[r] = mkznode(r0, zbrar, boolvar, true, m0), istore3[m1, indexblock([], [], 0)][index(m1).lnum] = indexblock(indx, lax, m3), istore = istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], 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), n0 < save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, btree-sub-clean(r, m0, zh), inv(istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)]), inv(istore3[m1, indexblock([], [], 0)]), inv(istore2), inv(istore3), inv(gstore1), inv(gstore2 \ ginval2), refsize-cons(istore3, as0 ∪ as), m ∈ istore3, r ∈ zh, n0 ≤ LEB_SIZE, as ⊆ dom nodes(istore3), as ⊆ alladrs, alladrs ⊆ dom nodes(istore3), as0 ⊆ dom nodes(istore3), istore2 ⊑ istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], istore2 ⊑ istore3[m1, indexblock([], [], 0)], istore2 ⊑ istore3, height = 0 → as = ∅ ⊦ ⟪apersistence_set_iblock_refsize# (index(m1).lnum, istore3[m1, indexblock([], [], 0)] [index(m1).lnum, istore3[m1, indexblock([], [], 0)] [index(m1).lnum, istore3[m1, indexblock([], [], 0)][index(m1).lnum].indlist:= (indx + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m1).lnum ] .ladrlist:= ( istore3[m1, indexblock([], [], 0)] [index(m1).lnum, istore3[m1, indexblock([], [], 0)][index(m1).lnum].indlist:= (indx + save(mkznode(r0, zbrar, boolvar, true, m0)) ') ] [index(m1).lnum ] .ladrlist + @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ') ] [index(m1).lnum ] .ref-size + save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino2, ginval, index(m1), syn ; istore); err0 := ESUCCESS; if err0 = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore, as0 ∪ (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as)) ∧ inv(istore) ∧ istore2 ⊑ istore ∧ m1 ∈ istore ∧ istore3 ⊑ istore ∧ r ∈ zh ∧ (err0 = ESUCCESS → ¬ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ as) ∧ dom nodes(istore) = dom nodes(istore3) ∪ (err0 = ESUCCESS ⊃ ∅ ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);∅) ∧ (( btree (rp, r, (err0 = ESUCCESS ⊃ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);adr1), height, err0 ≠ ESUCCESS, ri, nodes(istore), (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as), (err0 = ESUCCESS ⊃ (alladrs -- adr1) ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);alladrs), ok) * P) )(zh) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → ¬ zh[r].dirty)), dups(nx), adr1 ∈ as, m1 ∈ istore3

Rule argument

spec: ablock, inst: index-store name: elim seq: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m) subst: [iblock, indx, lax, m] → [istore3[m1, indexblock([], [], 0)][index(m1).lnum], indx, lax, m3]

Additional information

Used simplifier rules: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m); (elim) Used terms: istore3[m1, indexblock([], [], 0)][index(m1).lnum], indx, lax, m3