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

zh[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), ((btree(null, r, 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, r = null ∨ ¬ boolvar0 ⊦ ri = fi

User applied rule apply lemma

And obtained the following new goals

Proof step 9:
⊦ ((btree(rp0, r0, adr, height0, false, ri0, iast, as0, alladrs0, nstat) * P0))(zh0) ∧ ((btree(rp1, r1, adr, height1, false, ri1, iast, as1, alladrs1, nstat) * P1))(zh1) → height0 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1
Proof step 10:
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, 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, ((btree(null, r, 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, r = null ∨ ¬ boolvar0 ⊦ ri = fi

Rule argument

spec: <toplevel> name: btree-clean-fwd seq: ⊦ (( btree (rp0, r0, adr, height0, false, ri0, iast, as0, alladrs0, nstat) * P0) )(zh0) ∧ (( btree (rp1, r1, adr, height1, false, ri1, iast, as1, alladrs1, nstat) * P1) )(zh1) → height0 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1 subst: [rp0, r0, adr, height0, ri0, iast, as0, alladrs0, nstat, P0, zh0, rp1, r1, height1, ri1, as1, alladrs1, P1, zh1] → [null, r, adr, height, ri, nodes(istore), as, alladrs, ok, true, zh, null, null, height0, fi, as0, alladrs0, true, zh]

Additional information

Used terms: null, r, adr, height, ri, nodes(istore), as, alladrs, ok, true, zh, null, null, height0, fi, as0, alladrs0, true, zh