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Proof step 9 from proof btree-reset-root-frame (previous step)

(( 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 = ∅, ((true * P))(zh) ∧ (∃ r1, zh1, zbrar0, nused0. nused0 < BRANCH_SIZE ∧ unmodified(adr, mkznode(rp, zbrar0, height = 0, false, nused0), iast) ∧ (( r1 => mkznode(rp, zbrar0, height = 0, false, nused0) * bnode(r1, zbrar0, 0, nused0, nused0, height, false, ri, iast, alladrs -- adr, alladrs -- adr) * true * P) )(zh1))

User applied rule case distinction

And obtained the following new goals

Proof step 10:
(( 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 ∈ iast, adr ∈ alladrs, alladrs ⊆ dom iast, (r = null ⊃ P(zh);r0 = r ∧ zh0 = zh) ⊦ # alladrs = 0, alladrs = ∅, ∃ r1, zh1, zbrar0, nused0. nused0 < BRANCH_SIZE ∧ unmodified(adr, mkznode(rp, zbrar0, height = 0, false, nused0), iast) ∧ (( r1 => mkznode(rp, zbrar0, height = 0, false, nused0) * bnode(r1, zbrar0, 0, nused0, nused0, height, false, ri, iast, alladrs -- adr, alladrs -- adr) * true * P) )(zh1)

Rule argument

pos: right 3

Additional information

Used simplifier rules: maplet-null: ⊦ ((r => znd * P))(zh) → r ≠ null;% ⊦ P0(zh) → ((true * P0))(zh); (s)%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]% ⊦ ((P1 * P2))(zh) → ((true * P2))(zh); (s)