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Proof step 9 from proof btree-inv-root-null (previous step)

((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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ((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)
Proof step 11:
((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 ⊦ ri = fi, ((btree(null, null, adr, height0, false, fi, nodes(istore), as0, alladrs0, ok) * true))(zh)

Rule argument

spec: <toplevel> name: btree-crash seq: ⊦ (( 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) subst: [zh0, zh1, alladrs, as, iast0, fi, height, adr] → [zh, zh, alladrs0, as0, nodes(istore), fi, height0, adr] flags: <all paths>

Additional information

Used terms: zh, zh, alladrs0, as0, nodes(istore), fi, height0, adr