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Proof step 2 from proof btree-restrict-union-proper (previous step)

n < # asar ⊦ ((btree(rp, r, adr, height, dirty, ri, iast | union(asar, 0, # asar), asar[n], alladrs, nstat) * P))(zh) ↔ ((btree(rp, r, adr, height, dirty, ri, iast | asar[n], asar[n], alladrs, nstat) * P))(zh)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ((btree(rp, r0, adr, height, dirty0, ri, iast, as, alladrs, nstat) * P))(zh0) → ((btree(rp, r0, adr, height, dirty0, ri, iast | as, as, alladrs, nstat) * P))(zh0)
Proof step 4:
((btree(rp, r, adr, height, dirty, ri, iast, asar[n], alladrs, nstat) * P))(zh), n < # asar ⊦ ((btree(rp, r, adr, height, dirty, ri, iast | union(asar, 0, # asar), asar[n], alladrs, nstat) * P))(zh) ↔ true

Rule argument

spec: <toplevel> name: btree-istore-restrict-to-as seq: ⊦ (( btree (rp, r0, adr, height, dirty0, ri, iast, as, alladrs, nstat) * P) )(zh0) → (( btree (rp, r0, adr, height, dirty0, ri, iast | as, as, alladrs, nstat) * P) )(zh0) subst: [zh0, P, nstat, alladrs, as, iast, ri, dirty0, height, adr, r0, rp] → [zh, P, nstat, alladrs, asar[n], iast, ri, dirty, height, adr, r, rp] flags: <all paths>

Additional information

Used simplifier rules: btree-istore-restrict: ⊦ (( btree (rp, r0, adr, height, dirty0, ri, iast | as0, as, alladrs, nstat) * P) )(zh0) → (( btree (rp, r0, adr, height, dirty0, ri, iast, as, alladrs, nstat) * P) )(zh0);%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap] Used terms: zh, P, nstat, alladrs, asar[n], iast, ri, dirty, height, adr, r, rp