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Proof step 50 from proof btree-write-other (previous step)

adr0 ∈ as ↔ ¬ dirty0, (( r0 => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast, as -- adr0, alladrs -- adr0) * P) )(zh0), nsize(nused, nstat), unmodified(adr0, mkznode(rp, zbrar, false, dirty0, nused), iast), adr0 ∈ alladrs, dirty0 → dirty, (r = null ⊃ adr0 ∈ as ∧ P(zh);r0 = r ∧ zh0 = zh), ∀ 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 ⊦ # alladrs = 0, alladrs = ∅, adr ∈ as, unmodified(adr0, mkznode(rp, zbrar, false, dirty0, nused), iast[adr, ind]) ∧ (( r0 => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast[adr, ind], as -- adr0, alladrs -- adr0) * P) )(zh0)

User applied rule case distinction

And obtained the following new goals

Proof step 51:
adr0 ∈ as ↔ ¬ dirty0, (( r0 => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast, as -- adr0, alladrs -- adr0) * P) )(zh0), nsize(nused, nstat), unmodified(adr0, mkznode(rp, zbrar, false, dirty0, nused), iast), adr0 ∈ alladrs, dirty0 → dirty, (r = null ⊃ adr0 ∈ as ∧ P(zh);r0 = r ∧ zh0 = zh), ∀ 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 ⊦ # alladrs = 0, alladrs = ∅, (( r0 => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r0, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast[adr, ind], as -- adr0, alladrs -- adr0) * P) )(zh0), adr ∈ as

Rule argument

pos: right 4

Additional information

Used simplifier rules: ⊦ unmodified(adr, mkznode(rp, zbrar, bv, true, nused), iast); (s)%⊦ unmodified (adr0, mkznode(rp0, zbrar, boolvar, true, height), iast[adr, ind]) ↔ unmodified(adr0, mkznode(rp0, zbrar, boolvar, true, height), iast); (s)%adr ≠ adr0 ⊦ unmodified(adr0, znd, iast[adr, ind]) ↔ unmodified(adr0, znd, iast); (s)