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Proof step 9 from proof btree-inv-remove-refsize0 (previous step)

zh[rp] = mkznode(rp0, zbrar, boolvar, dirty, nused), ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), ((btree(null, rp, adr, height, false, ri, nodes(istore), alladrs, alladrs, ok) * true))(zh), inv(istore), inv(istore0), refsize-cons(istore0, alladrs0), refsize-cons(istore, alladrs), adr ∈ istore, alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), istore0 ⊑ istore, ¬ dirty ∨ rp = null, rp = null ∨ ¬ dirty ⊦ ((btree(null, rp, adr, height, false, ri, nodes(remove-refsize0(istore)), alladrs, alladrs, ok) * true))(zh) ∧ adr ∈ remove-refsize0(istore)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ iast0 | as ⊆ iast1 ∧ ((btree(rp, rp0, adr, height, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) → ((btree(rp, rp0, adr, height, dirty, ri, iast1, as, alladrs, nstat) * P))(zh)
Proof step 11:
zh[rp] = mkznode(rp0, zbrar, boolvar, dirty, nused), ((btree(null, rp, adr, height, false, ri, nodes(istore), alladrs, alladrs, ok) * true))(zh), ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), inv(istore0), inv(istore), refsize-cons(istore, alladrs), refsize-cons(istore0, alladrs0), adr ∈ istore, alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), istore0 ⊑ istore, rp = null ∨ ¬ dirty, ¬ dirty ∨ rp = null ⊦ ((btree(null, rp, adr, height, false, ri, nodes(remove-refsize0(istore)), alladrs, alladrs, ok) * true))(zh) ∧ adr ∈ remove-refsize0(istore), nodes(istore) | alladrs ⊆ nodes(remove-refsize0(istore)) ∧ ((btree(null, rp, adr, height, false, ri, nodes(istore), alladrs, alladrs, ok) * true))(zh)
Proof step 14:
zh[rp] = mkznode(rp0, zbrar, boolvar, dirty, nused), ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), ((btree(null, rp, adr, height, false, ri, nodes(istore), alladrs, alladrs, ok) * true))(zh), inv(istore0), inv(istore), refsize-cons(istore, alladrs), refsize-cons(istore0, alladrs0), adr ∈ istore, alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), nodes(istore) | alladrs ⊆ nodes(remove-refsize0(istore)), istore0 ⊑ istore, rp = null ∨ ¬ dirty, ¬ dirty ∨ rp = null ⊦ true ∧ adr ∈ remove-refsize0(istore)

Rule argument

spec: <toplevel> name: btree-istore-reduce-refed seq: ⊦ iast0 | as ⊆ iast1 ∧ (( btree (rp, rp0, adr, height, dirty, ri, iast0, as, alladrs, nstat) * P) )(zh) → (( btree (rp, rp0, adr, height, dirty, ri, iast1, as, alladrs, nstat) * P) )(zh) subst: [iast0, zh, P, nstat, alladrs, as, iast1, ri, dirty, height, adr, rp0, rp] → [nodes(istore), zh, true, ok, alladrs, alladrs, nodes(remove-refsize0(istore)), ri, false, height, adr, rp, null] flags: <all paths>

Additional information

Used terms: nodes(istore), zh, true, ok, alladrs, alladrs, nodes(remove-refsize0(istore)), ri, false, height, adr, rp, null