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Proof step 27 from proof btree-inv-crash (previous step)

istore0[@(m, m0, m1)] = istore[@(m, m0, m1)], crash(istore, istore0)[m] = indexblock(indlist, lax, m2), remove-refsize0(istore0) = istore0, ((btree(null, null, @(m, m0, m1), height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh0), ((btree(null, rp, @(m, m0, m1), height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), (( 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), nused < BRANCH_SIZE, inv(istore), refsize-cons(istore, as), refsize-cons(istore0, as0), unmodified(@(m, m0, m1), mkznode(null, zbrar, height0 = 0, false, nused), nodes(istore0)), m ∈ istore, m ∈ istore0, @(m, m0, m1) ∈ istore0, @(m, m0, m1) ∈ istore, @(m, m0, m1) ∈ as0, @(m, m0, m1) ∈ alladrs0, nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))), as0 ⊆ alladrs0, as0 ⊆ dom nodes(istore0), as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), as0 ⊆ dom nodes(istore), istore0 ⊑ istore ⊦ # as0 = 0, # alladrs0 = 0, alladrs0 = ∅, as0 = ∅, @(m0, m1) ∈ lax, @(m, m0, m1) ∈ remove-refsize0(crash(istore, istore0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ n ∈ istore0 → crash(istore, istore0)[n] = indexblock(istore[n].indlist, istore[n].ladrlist, istore0[n].ref-size)
Proof step 29:
istore0[@(m, m0, m1)] = istore[@(m, m0, m1)], indexblock(istore[m].indlist, istore[m].ladrlist, istore0[m].ref-size) = indexblock(indlist, lax, m2), 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) ∈ lax

Rule argument

spec: apersistence-base name: crash-index-at seq: ⊦ n ∈ istore0 → crash(istore, istore0)[n] = indexblock (istore[n].indlist, istore[n].ladrlist, istore0[n].ref-size) subst: [n, istore0, istore] → [m, istore0, istore] flags: <all paths>

Additional information

Used terms: m, istore0, istore