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Proof step 2 from proof btree-inv-clean-commit (previous step)

btree-inv(rp, adr, istore, istore0, zh, ri, fi), istore0 ⊑ istore, rp = null ∨ ¬ zh[rp].dirty ⊦ btree-inv(rp, adr, istore, istore, zh, ri, ri)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh), ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh), refsize-cons(istore0, as0), refsize-cons(istore, as), adr ∈ istore, as0 ⊆ alladrs0, as0 ⊆ dom nodes(istore0), as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), as0 ⊆ dom nodes(istore), istore0 ⊑ istore, rp = null ∨ ¬ zh[rp].dirty ⊦ (∃ height1, dirty0, as1, alladrs1. ((btree(null, rp, adr, height1, dirty0, ri, nodes(istore), as1, alladrs1, ok) * true))(zh) ∧ refsize-cons(istore, as1) ∧ alladrs1 ⊆ dom nodes(istore)) ∧ (∃ height, as, alladrs. ((btree(null, null, adr, height, false, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore, as) ∧ alladrs ⊆ dom nodes(istore))

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-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;%sub-trans: ⊦ as ⊆ as0 ∧ as0 ⊆ as1 → as ⊆ as1; (forward) from specification set-basic[node-store]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]