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Proof step 7 from proof btree-inv-clean-commit (previous step)

zh[rp] = mkznode(r, zbrar, boolvar, boolvar0, m), ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh), ((btree(null, rp, 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, rp = null ∨ ¬ boolvar0 ⊦ (∃ height1, dirty0, as1, alladrs1. ((btree(null, rp, adr, height1, dirty0, ri, nodes(istore), as1, alladrs1, ok) * true))(zh) ∧ refsize-cons(istore, as1) ∧ alladrs1 ⊆ dom nodes(istore)) ∧ (∃ height, as, alladrs. ((btree(null, null, adr, height, false, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore, as) ∧ alladrs ⊆ dom nodes(istore))

User applied rule apply lemma

And obtained the following new goals

Proof step 8:
⊦ 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)
Proof step 9:
zh[rp] = mkznode(r, zbrar, boolvar, boolvar0, m), ((btree(null, rp, 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, nodes(istore0) ⊆ nodes(istore) ∧ ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh) → ((btree(null, null, adr, height0, false, fi, nodes(istore), as0, alladrs0, ok) * true))(zh), rp = null ∨ ¬ boolvar0 ⊦ (∃ height1, dirty0, as1, alladrs1. ((btree(null, rp, adr, height1, dirty0, ri, nodes(istore), as1, alladrs1, ok) * true))(zh) ∧ refsize-cons(istore, as1) ∧ alladrs1 ⊆ dom nodes(istore)) ∧ (∃ height, as, alladrs. ((btree(null, null, adr, height, false, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore, as) ∧ alladrs ⊆ dom nodes(istore))

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, iast1, rp, r0, adr, height, dirty0, ri, as, alladrs, nstat, P, zh0] → [nodes(istore0), nodes(istore), null, null, adr, height0, false, fi, as0, alladrs0, ok, true, zh]

Additional information

Used terms: nodes(istore0), nodes(istore), null, null, adr, height0, false, fi, as0, alladrs0, ok, true, zh