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Proof step 8 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 ∈ iast, adr ∈ alladrs, alladrs ⊆ dom iast, (r = null ⊃ P(zh);r0 = r ∧ zh0 = zh) ⊦ # alladrs = 0, alladrs = ∅, ∃ r, zh1, zbrar, dirty, nused. (null = null ⊃ ¬ dirty ∧ ((true * P))(zh);r = null ∧ zh1 = zh) ∧ (dirty → false) ∧ (adr ∈ alladrs ↔ ¬ dirty) ∧ adr ∈ alladrs ∧ nsize(nused, ok) ∧ unmodified(adr, mkznode(rp, zbrar, height = 0, dirty, nused), iast) ∧ (( r => mkznode(rp, zbrar, height = 0, dirty, nused) * bnode(r, zbrar, 0, nused, nused, height, dirty, ri, iast, alladrs -- adr, alladrs -- adr) * true * P) )(zh1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
(( 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))

Rule argument

Additional information

Used simplifier rules: ⊦ nsize(nused, ok) ↔ nused < BRANCH_SIZE; (s)