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Proof step 34 from proof btree-inv-crash (previous step)

remove-refsize0(istore0) = istore0, ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh0), ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh1), inv(istore), refsize-cons(istore0, as0), refsize-cons(istore, as), adr ∈ istore, as0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, as0 ⊆ dom nodes(istore0), as0 ⊆ alladrs0, nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))), istore0 ⊑ istore ⊦ dom nodes(istore) ⊆ dom nodes(remove-refsize0(crash(istore, istore0))), alladrs0 ⊆ dom nodes(remove-refsize0(crash(istore, istore0))), alladrs0 ⊆ dom nodes(crash(istore, istore0)) ∧ refsize-cons(crash(istore, istore0), alladrs0) ∧ inv(crash(istore, istore0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
remove-refsize0(istore0) = istore0, ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh1), ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh0), ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), inv(istore), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), adr ∈ istore, alladrs0 ⊆ dom nodes(istore0), nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))), as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), istore0 ⊑ istore ⊦ dom nodes(istore) ⊆ dom nodes(crash(istore, istore0)), dom nodes(istore0) ⊆ dom nodes(remove-refsize0(crash(istore, istore0))), dom nodes(istore0) ⊆ dom nodes(crash(istore, istore0)), alladrs0 ⊆ dom nodes(crash(istore, istore0)), alladrs0 ⊆ dom nodes(remove-refsize0(crash(istore, istore0))), dom nodes(istore) ⊆ dom nodes(remove-refsize0(crash(istore, istore0)))

Rule argument

Additional information

Used simplifier rules: 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;%sub-ntrans: ⊦ as ⊆ as0 ∧ ¬ as ⊆ as1 → ¬ as0 ⊆ as1; (forward) from specification set-basic[node-store]%sub-idem: ⊦ as ⊆ as; 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]% ⊦ istore0 ⊑ istore ∧ inv(istore) → inv(crash(istore, istore0)); (ss)%⊦ refsize-cons(crash(istore1, istore0), as) ↔ refsize-cons(istore0, as); (s)