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Proof step 20 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 ⊦ ∃ height, as, alladrs. ((btree(null, null, adr, height, false, fi, nodes(remove-refsize0(istore)), as, alladrs, ok) * true))(zh) ∧ refsize-cons(remove-refsize0(istore), as) ∧ alladrs ⊆ dom nodes(remove-refsize0(istore))

User applied rule apply lemma

And obtained the following new goals

Proof step 21:
⊦ iast0 ⊆ iast1 ∧ ((btree(rp0, r0, adr, height0, false, ri0, iast0, as0, alladrs0, nstat) * P0))(zh0) ∧ ((btree(rp1, r1, adr, height1, false, ri1, iast1, as1, alladrs1, nstat) * P1))(zh1) → height0 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1
Proof step 22:
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, nodes(istore0) ⊆ nodes(istore) ∧ ((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) → height0 = height ∧ alladrs0 = alladrs ∧ fi = ri ∧ alladrs0 = alladrs, rp = null ∨ ¬ dirty, ¬ dirty ∨ rp = null ⊦ ∃ height, as, alladrs. ((btree(null, null, adr, height, false, fi, nodes(remove-refsize0(istore)), as, alladrs, ok) * true))(zh) ∧ refsize-cons(remove-refsize0(istore), as) ∧ alladrs ⊆ dom nodes(remove-refsize0(istore))

Rule argument

spec: <toplevel> name: btree-clean-fwd-strong seq: ⊦ iast0 ⊆ iast1 ∧ (( btree (rp0, r0, adr, height0, false, ri0, iast0, as0, alladrs0, nstat) * P0) )(zh0) ∧ (( btree (rp1, r1, adr, height1, false, ri1, iast1, as1, alladrs1, nstat) * P1) )(zh1) → height0 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1 subst: [iast0, iast1, rp0, r0, adr, height0, ri0, as0, alladrs0, nstat, P0, zh0, rp1, r1, height1, ri1, as1, alladrs1, P1, zh1] → [nodes(istore0), nodes(istore), null, null, adr, height0, fi, alladrs0, alladrs0, ok, true, zh, null, rp, height, ri, alladrs, alladrs, true, zh]

Additional information

Used terms: nodes(istore0), nodes(istore), null, null, adr, height0, fi, alladrs0, alladrs0, ok, true, zh, null, rp, height, ri, alladrs, alladrs, true, zh