[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 28 from proof inv-commit-rec (previous step)

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), 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, 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-inv(r0, @(m1, m2, m3), istore2, istore2, zh0, ri, ri) ∧ btree-inv(r0, adr1, istore2[m1, indexblock(indx, lax, m4 - m3)], istore0, zh0[r0, mkznode(r1, zbrar0, boolvar0, true, m5)], ri, fi)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ btree-inv(r, adr, istore, istore0, zh, ri, fi) ↔ (∃ height, dirty, as, alladrs. ((btree(null, r, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore, as) ∧ adr ∈ istore ∧ alladrs ⊆ dom nodes(istore)) ∧ (∃ height, dirty, as, alladrs. ((btree(null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore))
Proof step 30:
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, ( (∃ height, dirty, as, alladrs. ((btree(null, r0, @(m1, m2, m3), height, dirty, ri, nodes(istore2), as, alladrs, ok) * true))(zh0) ∧ refsize-cons(istore2, as) ∧ @(m1, m2, m3) ∈ istore2 ∧ alladrs ⊆ dom nodes(istore2)) ∧ (∃ height, dirty, as, alladrs. ((btree(null, null, @(m1, m2, m3), height, false, ri, nodes(istore2), as, alladrs, ok) * true))(zh0) ∧ refsize-cons(istore2, as) ∧ alladrs ⊆ dom nodes(istore2))) ∧ btree-inv(r0, adr1, istore2[m1, indexblock(indx, lax, m4 - m3)], istore0, zh0[r0, mkznode(r1, zbrar0, boolvar0, true, m5)], ri, fi)

Rule argument

spec: btree-inv name: btree-inv seq: ⊦ btree-inv(r, adr, istore, istore0, zh, ri, fi) ↔ (∃ height, dirty, as, alladrs. (( btree (null, r, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore, as) ∧ adr ∈ istore ∧ alladrs ⊆ dom nodes(istore)) ∧ (∃ height, dirty, as, alladrs. (( btree (null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore)) subst: [fi, ri, zh, istore0, istore, adr, r] → [ri, ri, zh0, istore2, istore2, @(m1, m2, m3), r0] flags: <all paths>

Additional information

Used terms: ri, ri, zh0, istore2, istore2, @(m1, m2, m3), r0