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Proof step 8 from proof btree-inv-root-null (previous step)

((btree(null, null, 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, ((btree(null, null, adr, height, false, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ ((btree(null, null, adr, height0, false, fi, nodes(istore), as0, alladrs0, ok) * true))(zh) → height = height0 ∧ as = as0 ∧ ri = fi ∧ alladrs = alladrs0 ⊦ ri = fi

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh), ((btree(null, null, adr, height, false, 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 ⊦ ri = fi, ((btree(null, null, adr, height0, false, fi, nodes(istore), as0, alladrs0, ok) * true))(zh)

Rule argument

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);%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]