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Proof step 10 from proof btree-inv-alloc (previous step)

((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh0), ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), inv(istore), refsize-cons(istore[n, indexblock(indx, lax, 0)], as), refsize-cons(istore0, alladrs0), refsize-cons(istore, as), adr ∈ istore, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0) ⊦ ((btree(null, rp, adr, height, dirty, ri, nodes(istore[n, indexblock(indx, lax, 0)]), as, alladrs, ok) * true))(zh0), n ∈ istore

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ iast0 | as ⊆ iast1 ∧ ((btree(rp, rp0, adr, height, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) → ((btree(rp, rp0, adr, height, dirty, ri, iast1, as, alladrs, nstat) * P))(zh)
Proof step 12:
((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh0), inv(istore), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), refsize-cons(istore[n, indexblock(indx, lax, 0)], as), adr ∈ istore, alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs ⊦ ((btree(null, rp, adr, height, dirty, ri, nodes(istore[n, indexblock(indx, lax, 0)]), as, alladrs, ok) * true))(zh0), n ∈ istore, nodes(istore) | as ⊆ nodes(istore[n, indexblock(indx, lax, 0)]) ∧ ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0)

Rule argument

spec: <toplevel> name: btree-istore-reduce-refed seq: ⊦ iast0 | as ⊆ iast1 ∧ (( btree (rp, rp0, adr, height, dirty, ri, iast0, as, alladrs, nstat) * P) )(zh) → (( btree (rp, rp0, adr, height, dirty, ri, iast1, as, alladrs, nstat) * P) )(zh) subst: [iast0, zh, P, nstat, alladrs, as, iast1, ri, dirty, height, adr, rp0, rp] → [nodes(istore), zh0, true, ok, alladrs, as, nodes(istore[n, indexblock(indx, lax, 0)]), ri, dirty, height, adr, rp, null] flags: <all paths>

Additional information

Used terms: nodes(istore), zh0, true, ok, alladrs, as, nodes(istore[n, indexblock(indx, lax, 0)]), ri, dirty, height, adr, rp, null