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Proof step 43 from proof inv-commit-rec (previous step)

istore2[m1] = indexblock(indx, lax, m4), zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore[adr1] = istore2[adr1], zh0[r0] = mkznode(r1, zbrar0, boolvar0, false, m5), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, null, adr1, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, r0, @(m1, m2, m3), height, false, ri, nodes(istore2) | alladrs1, alladrs1, alladrs1, ok) * true))(zh0), inv(istore2), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), refsize-cons(istore2, alladrs1), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), @(m1, m2, m3) ∈ istore2, @(m1, m2, m3) ∈ alladrs1, adr1 ∈ istore2, r0 ∈ zh0, m ∈ istore, adr1 ∈ istore, r0 ∈ zh, m ∈ istore2, m6 ∈ istore2, alladrs1 ∩ dom nodes(istore) ⊆ alladrs, alladrs1 ⊆ dom nodes(istore2), alladrs1 ∩ dom nodes(istore) ⊆ as, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), istore ⊑ istore2, istore0 ⊑ istore2, istore0 ⊑ istore, height = 0 → alladrs1 = ∅ ++ @(m1, m2, m3), height = 0 → as = ∅ ⊦ # alladrs1 = 0, alladrs1 = ∅, dups(nx), adr1 ∈ as, ((btree(null, r0, adr1, height, true, ri, nodes(istore2), alladrs1 -- @(m1, m2, m3), (alladrs1 -- @(m1, m2, m3)) ++ adr1, ok) * true) )(zh0[r0, mkznode(r1, zbrar0, boolvar0, true, m5)]) ∧ refsize-cons(istore2[m1, indexblock(indx, lax, m4 - m3)], alladrs1 -- @(m1, m2, m3)) ∧ adr1 ∈ istore2[m1, indexblock(indx, lax, m4 - m3)] ∧ (alladrs1 -- @(m1, m2, m3)) ++ adr1 ⊆ dom nodes(istore2), ¬ m1 ∈ istore2 ∧ adr1 ∈ istore2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
zh0[r0] = mkznode(r1, zbrar0, boolvar0, false, m5), istore[adr1] = istore2[adr1], zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore2[m1] = indexblock(indx, lax, m4), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, r0, @(m1, m2, m3), height, false, ri, nodes(istore2) | alladrs1, alladrs1, alladrs1, ok) * true))(zh0), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, null, adr1, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(istore2), inv(indexblock(indx, lax, m4)), refsize-cons(istore0, alladrs0), refsize-cons(istore, as), refsize-cons(istore2, alladrs1), m6 ∈ istore2, m ∈ istore2, r0 ∈ zh, adr1 ∈ istore, m ∈ istore, r0 ∈ zh0, adr1 ∈ istore2, @(m1, m2, m3) ∈ alladrs1, @(m1, m2, m3) ∈ istore2, m1 ∈ istore2, alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, alladrs1 ∩ dom nodes(istore) ⊆ as, alladrs1 ⊆ dom nodes(istore2), alladrs1 ∩ dom nodes(istore) ⊆ alladrs, istore0 ⊑ istore, istore0 ⊑ istore2, istore ⊑ istore2, height = 0 → as = ∅, height = 0 → alladrs1 = ∅ ++ @(m1, m2, m3) ⊦ # alladrs1 = 0, alladrs1 = ∅, dups(nx), adr1 ∈ as, ((btree(null, r0, adr1, height, true, ri, nodes(istore2), alladrs1 -- @(m1, m2, m3), (alladrs1 -- @(m1, m2, m3)) ++ adr1, ok) * true) )(zh0[r0, mkznode(r1, zbrar0, boolvar0, true, m5)]) ∧ (alladrs1 -- @(m1, m2, m3)) ++ adr1 ⊆ dom nodes(istore2)

Rule argument

Additional information

Used simplifier rules: fwd-inv-iblock: ⊦ inv(istore) ∧ n ∈ istore ∧ istore[n] = iblock → inv(iblock); (forward) from specification apersistence-base%istore[n].indlist = indx, istore[n].ladrlist = lax ⊦ n ∈ istore → (adr ∈ istore[n, indexblock(indx, lax, m)] ↔ adr ∈ istore); (s)% ⊦ indexblock(indx, lax, m).ladrlist = lax; (s)% ⊦ indexblock(indx, lax, m).indlist = indx; (s)%⊦ refsize-cons(istore, as) ∧ @(m, m0, m1) ∈ as ∧ m ∈ istore ∧ istore[m] = indexblock(indx, lax, n0) → refsize-cons (istore[m, indexblock(indx, lax, n0 - m1)], as -- @(m, m0, m1)); (ss)