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Proof step 10 from proof btree-istore-reduce-refed (previous step)

# zbrar = BRANCH_SIZE, as -- adr = ∅, adr ∈ as ↔ ¬ dirty0, ((r => mkznode(rp, zbrar, true, dirty0, nused) * P))(zh0), nsize(nused, nstat), sorted(zbrar, 0, nused), unmodified(adr, mkznode(rp, zbrar, true, dirty0, nused), iast0), nused ≤ BRANCH_SIZE, as ⊆ ∅ ++ adr, as ⊆ dom iast0, iast0 | as ⊆ iast1, dirty0 → dirty, (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh) ⊦ ∃ 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, true, dirty1, nused0), iast1) ∧ nused0 ≤ # zbrar0 ∧ # zbrar0 = BRANCH_SIZE ∧ sorted(zbrar0, 0, nused0) ∧ payload(zbrar, 0, nused) = payload(zbrar0, 0, nused0) ∧ ((P * r0 => mkznode(rp, zbrar0, true, dirty1, nused0)))(zh1)

User applied rule exists right

And obtained the following new goals

Proof step 11:
# zbrar = BRANCH_SIZE, as -- adr = ∅, adr ∈ as ↔ ¬ dirty0, ((r => mkznode(rp, zbrar, true, dirty0, nused) * P))(zh0), nsize(nused, nstat), sorted(zbrar, 0, nused), unmodified(adr, mkznode(rp, zbrar, true, dirty0, nused), iast0), nused ≤ BRANCH_SIZE, iast0 | as ⊆ iast1, as ⊆ dom iast0, as ⊆ ∅ ++ adr, dirty0 → dirty, (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh) ⊦ (rp0 = null ⊃ ¬ dirty0 ∧ P(zh);r = rp0 ∧ zh0 = zh) ∧ (dirty0 → dirty) ∧ (adr ∈ as ↔ ¬ dirty0) ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp, zbrar, true, dirty0, nused), iast1) ∧ nused ≤ # zbrar ∧ # zbrar = BRANCH_SIZE ∧ sorted(zbrar, 0, nused) ∧ payload(zbrar, 0, nused) = payload(zbrar, 0, nused) ∧ ((P * r => mkznode(rp, zbrar, true, dirty0, nused)))(zh0)

Rule argument

pos: right 1 terms: r, zh0, zbrar, dirty0, nused abort: F discard: T computed: T

Additional information

Used terms: r, zh0, zbrar, dirty0, nused