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Proof step 5 from proof btree-inv-root-null-or-clean (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh), ((btree(null, r, 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, r = null ∨ ¬ boolvar0 ⊦ ri = fi

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: btree-null-or-clean-below seq: ⊦ r = null ∨ ¬ zh0[r].dirty → ( (( btree (rp, r, adr, height, dirty, ri, iast, as, alladrs, nstat) * P) )(zh0) ↔ (( btree (rp, r, adr, height, false, ri, iast, as, alladrs, nstat) * P) )(zh0)) subst: [zh0, P, nstat, alladrs, as, iast, ri, dirty, height, adr, r, rp] → [zh, true, ok, alladrs, as, nodes(istore), ri, dirty, height, adr, r, null] flags: <all paths>

Additional information

Used simplifier rules: btree-root-in-heap: ⊦ r ≠ null ∧ (( btree (rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → r ∈ zh;%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%nonnull: ⊦ r ∈ zh → r ≠ null; from specification heap[zheap]% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).dirty ↔ boolvar0; (s) Used terms: zh, true, ok, alladrs, as, nodes(istore), ri, dirty, height, adr, r, null