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Proof step 2 from proof btree-inv-alloc (previous step)

btree-inv(rp, adr, istore, istore0, zh0, ri, fi), inv(istore) ⊦ btree-inv(rp, adr, istore[n, indexblock(indx, lax, 0)], istore0, zh0, ri, fi), n ∈ istore

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh0), inv(istore), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), adr ∈ istore, alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs ⊦ n ∈ istore, (∃ height1, dirty0, as1, alladrs1. ((btree(null, rp, adr, height1, dirty0, ri, nodes(istore[n, indexblock(indx, lax, 0)]), as1, alladrs1, ok) * true))(zh0) ∧ refsize-cons(istore[n, indexblock(indx, lax, 0)], as1) ∧ alladrs1 ⊆ dom nodes(istore[n, indexblock(indx, lax, 0)])) ∧ (∃ height, as, alladrs. ((btree(null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true))(zh0) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore[n, indexblock(indx, lax, 0)]))

Rule argument

Additional information

Used simplifier rules: btree-inv: ⊦ btree-inv(r, adr, istore, istore0, zh, ri, fi) ↔ (∃ height, dirty, as, alladrs. (( btree (null, r, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore, as) ∧ adr ∈ istore ∧ alladrs ⊆ dom nodes(istore)) ∧ (∃ height, dirty, as, alladrs. (( btree (null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore));%btree-clean-alladrs: ⊦ (( btree(rp, r, adr, height, false, ri, iast, as, alladrs, nstat) * P) )(zh) → as = alladrs;%btree-refed-subseteq-alladrs: ⊦ (( btree(rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ alladrs;%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast;% ⊦ as ⊆ as; (s)%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]% ⊦ ¬ n ∈ istore ∧ adr ∈ istore → adr ∈ istore[n, iblock]; (ss)