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Proof step 5 from proof btree-restrict-union-proper (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 7:
((btree(rp, r, adr, height, dirty, ri, iast, asar[n], alladrs, nstat) * P))(zh), n < # asar, asar[n] ⊆ alladrs, asar[n] ⊆ dom iast ⊦ ((btree(rp, r, adr, height, dirty, ri, iast | union(asar, 0, # asar), asar[n], alladrs, nstat) * P))(zh), iast | asar[n] ⊆ iast | union(asar, 0, # asar) ∧ ((btree(rp, r, adr, height, dirty, ri, iast, asar[n], alladrs, nstat) * P))(zh)

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] → [iast, zh, P, nstat, alladrs, asar[n], iast | union(asar, 0, # asar), ri, dirty, height, adr, r, rp] flags: <all paths>

Additional information

Used terms: iast, zh, P, nstat, alladrs, asar[n], iast | union(asar, 0, # asar), ri, dirty, height, adr, r, rp