[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 30 from proof btree-inv-crash (previous step)

istore0[@(m, m0, m1)] = istore[@(m, m0, m1)], remove-refsize0(istore0) = istore0, (( r => mkznode(null, zbrar, height0 = 0, false, nused) * bnode(r, zbrar, 0, nused, nused, height0, false, fi, nodes(istore0), as0 -- @(m, m0, m1), alladrs0 -- @(m, m0, m1)) * true) )(zh), ((btree(null, rp, @(m, m0, m1), height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), ((btree(null, null, @(m, m0, m1), height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh0), nused < BRANCH_SIZE, inv(istore), refsize-cons(istore0, as0), refsize-cons(istore, as), unmodified(@(m, m0, m1), mkznode(null, zbrar, height0 = 0, false, nused), nodes(istore0)), @(m, m0, m1) ∈ alladrs0, @(m, m0, m1) ∈ as0, @(m, m0, m1) ∈ istore, @(m, m0, m1) ∈ istore0, m ∈ istore, m ∈ istore0, as0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, as0 ⊆ dom nodes(istore0), as0 ⊆ alladrs0, nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))), istore0 ⊑ istore ⊦ # alladrs0 = 0, # as0 = 0, alladrs0 = ∅, as0 = ∅, @(m, m0, m1) ∈ remove-refsize0(crash(istore, istore0)), @(m0, m1) ∈ istore[m].ladrlist

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: ablock, inst: index-store name: elim seq: ⊦ (indlist = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indlist, lax, m) subst: [iblock, indlist, lax, m] → [istore[m], indlist, lax, m2]

Additional information

Used simplifier rules: ⊦ istore[n] = indexblock(indlist, lax, m0) ∧ @(n, n0, n1) ∈ istore → @(n0, n1) ∈ lax; (ss)%⊦ (indlist = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indlist, lax, m); (elim) Used terms: istore[m], indlist, lax, m2