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Proof step 23 from proof btree-istore-reduce-refed (previous step)

adr ∈ as ↔ ¬ dirty0, ((r => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast0, as -- adr, alladrs -- adr) * P) )(zh0), nsize(nused, nstat), unmodified(adr, mkznode(rp, zbrar, false, dirty0, nused), iast0), adr ∈ alladrs, iast0 | as ⊆ iast1, as ⊆ dom iast0, as ⊆ alladrs, dirty0 → dirty, (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh), ∀ rp, rp0, adr, dirty, ri, iast0, as, alladrs, nstat, P, zh, iast1. ((btree(rp, rp0, adr, height0, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) ∧ iast0 | as ⊆ iast1 ∧ as ⊆ dom iast0 ∧ as ⊆ alladrs → ((btree(rp, rp0, adr, height0, dirty, ri, iast1, as, alladrs, nstat) * P))(zh) ⊦ # alladrs = 0, alladrs = ∅, ∃ r, zh1, zbrar, dirty1, nused. (rp0 = null ⊃ ¬ dirty1 ∧ P(zh);r = rp0 ∧ zh1 = zh) ∧ (dirty1 → dirty) ∧ (adr ∈ as ↔ ¬ dirty1) ∧ adr ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar, height0 + 1 = 0, dirty1, nused), iast1) ∧ (( r => mkznode(rp, zbrar, height0 + 1 = 0, dirty1, nused) * bnode(r, zbrar, 0, nused, nused, height0 + 1, dirty1, ri, iast1, as -- adr, alladrs -- adr) * P) )(zh1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
adr ∈ as ↔ ¬ dirty0, ((r => mkznode(rp, zbrar, false, dirty0, nused) * bnode(r, zbrar, 0, nused, nused, height0 + 1, dirty0, ri, iast0, as -- adr, alladrs -- adr) * P) )(zh0), nsize(nused, nstat), unmodified(adr, mkznode(rp, zbrar, false, dirty0, nused), iast0), adr ∈ alladrs, as ⊆ alladrs, as ⊆ dom iast0, iast0 | as ⊆ iast1, dirty0 → dirty, (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh), ∀ rp, rp0, adr, dirty, ri, iast0, as, alladrs, nstat, P, zh, iast1. ((btree(rp, rp0, adr, height0, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) ∧ iast0 | as ⊆ iast1 ∧ as ⊆ dom iast0 ∧ as ⊆ alladrs → ((btree(rp, rp0, adr, height0, dirty, ri, iast1, as, alladrs, nstat) * P))(zh) ⊦ # alladrs = 0, alladrs = ∅, ∃ r0, zh1, zbrar0, dirty1, nused0. (rp0 = null ⊃ ¬ dirty1 ∧ P(zh);r0 = rp0 ∧ zh1 = zh) ∧ (dirty1 → dirty) ∧ (adr ∈ as ↔ ¬ dirty1) ∧ nsize(nused0, nstat) ∧ unmodified(adr, mkznode(rp, zbrar0, false, dirty1, nused0), iast1) ∧ (( r0 => mkznode(rp, zbrar0, false, dirty1, nused0) * bnode(r0, zbrar0, 0, nused0, nused0, height0 + 1, dirty1, ri, iast1, as -- adr, alladrs -- adr) * P) )(zh1)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)