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Proof step 5 from proof btree-reset-root-frame (previous step)

alladrs ⊆ dom iast, ∃ r1, zh1, zbrar, dirty, nused. (r = null ⊃ ¬ dirty ∧ P(zh);r1 = r ∧ zh1 = zh) ∧ (dirty → false) ∧ (adr ∈ alladrs ↔ ¬ dirty) ∧ adr ∈ alladrs ∧ nsize(nused, ok) ∧ unmodified(adr, mkznode(rp, zbrar, height = 0, dirty, nused), iast) ∧ (( r1 => mkznode(rp, zbrar, height = 0, dirty, nused) * bnode(r1, zbrar, 0, nused, nused, height, dirty, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh1) ⊦ ((btree(rp, null, adr, height, false, ri, iast, alladrs, alladrs, ok) * true * P))(zh)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
(( r0 => mkznode(rp, zbrar, height = 0, false, nused) * bnode(r0, zbrar, 0, nused, nused, height, false, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh0), nused < BRANCH_SIZE, unmodified(adr, mkznode(rp, zbrar, height = 0, false, nused), iast), adr ∈ alladrs, adr ∈ iast, alladrs ⊆ dom iast, (r = null ⊃ P(zh);r0 = r ∧ zh0 = zh) ⊦ # alladrs = 0, alladrs = ∅, ((btree(rp, null, adr, height, false, ri, iast, alladrs, alladrs, ok) * true * P))(zh)

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]% ⊦ adr ∈ dom iast ↔ adr ∈ iast; (s)% ⊦ BRANCH_SIZE ≠ 0; (s)%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]%sub-in: ⊦ adr ∈ as ∧ as ⊆ as0 → adr ∈ as0; (forward) from specification set-basic[node-store]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ nsize(nused, ok) ↔ nused < BRANCH_SIZE; (s)