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Proof step 11 from proof btree-inv-root-null-or-clean (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), ((btree(null, r, adr, height, false, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh), refsize-cons(istore, as), refsize-cons(istore0, as0), 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, istore0 ⊑ istore, r = null ∨ ¬ boolvar0 ⊦ ri = fi, ((btree(null, null, adr, height0, false, fi, nodes(istore), as0, alladrs0, ok) * true))(zh)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: btree-istore-reduce seq: ⊦ iast0 ⊆ iast1 ∧ (( btree (rp, r0, adr, height, dirty0, ri, iast0, as, alladrs, nstat) * P) )(zh0) → (( btree (rp, r0, adr, height, dirty0, ri, iast1, as, alladrs, nstat) * P) )(zh0) subst: [iast0, zh0, P, nstat, alladrs, as, iast1, ri, dirty0, height, adr, r0, rp] → [nodes(istore0), zh, true, ok, alladrs0, as0, nodes(istore), fi, false, height0, adr, null, null] flags: <all paths>

Additional information

Used simplifier rules: btree-crash: ⊦ (( btree (null, null, adr, height, false, fi, iast0, as, alladrs, ok) * true) )(zh0) → (( btree (null, null, adr, height, false, fi, iast0, as, alladrs, ok) * true) )(zh1);% ⊦ istore ⊑ istore0 → nodes(istore) ⊆ nodes(istore0); (ss)%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap] Used terms: nodes(istore0), zh, true, ok, alladrs0, as0, nodes(istore), fi, false, height0, adr, null, null