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Proof step 2 from proof btree-write-other (previous step)

⊦ ((btree(rp, r, adr0, height, dirty, ri, iast[adr, ind], as, alladrs, nstat) * P))(zh) ↔ ((btree(rp, r, adr0, height, dirty, ri, iast, as, alladrs, nstat) * P))(zh), adr ∈ as

User applied rule structural induction

And obtained the following new goals

Proof step 3:
⊦ ((btree(rp, r, adr0, 0, dirty, ri, iast[adr, ind], as, alladrs, nstat) * P))(zh) ↔ ((btree(rp, r, adr0, 0, dirty, ri, iast, as, alladrs, nstat) * P))(zh), adr ∈ as
Proof step 14:
∀ rp, r, adr0, dirty, ri, iast, adr, ind, as, alladrs, nstat, P, zh. ( ((btree(rp, r, adr0, height0, dirty, ri, iast[adr, ind], as, alladrs, nstat) * P))(zh) ↔ ((btree(rp, r, adr0, height0, dirty, ri, iast, as, alladrs, nstat) * P))(zh)) ∨ adr ∈ as ⊦ ((btree(rp, r, adr0, height0 +1, dirty, ri, iast[adr, ind], as, alladrs, nstat) * P))(zh) ↔ ((btree(rp, r, adr0, height0 +1, dirty, ri, iast, as, alladrs, nstat) * P))(zh), adr ∈ as

Rule argument

indvar: height

Additional information

Used simplifier rules: nat freely generated by 0, +1;;