[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 36 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, ∃ height, 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)

User applied rule exists right

And obtained the following new goals

Proof step 37:
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(null, null, @(m1, m2, m3), height, false, ri, nodes(istore2), alladrs1, alladrs1, ok) * true))(zh0) ∧ refsize-cons(istore2, alladrs1) ∧ alladrs1 ⊆ dom nodes(istore2)

Rule argument

pos: right 5 terms: height, alladrs1, alladrs1 abort: F discard: T computed: F

Additional information

Used terms: height, alladrs1, alladrs1