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Proof step 11 from proof btree-inv-remove-refsize0 (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
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 ⊦ nodes(istore) | alladrs ⊆ nodes(remove-refsize0(istore)), ((btree(null, rp, adr, height, false, ri, nodes(remove-refsize0(istore)), alladrs, alladrs, ok) * true))(zh) ∧ adr ∈ remove-refsize0(istore)

Rule argument

Additional information

Used simplifier rules: ⊦ ((P1 * P2))(zh) → ((true * P2))(zh); (s)%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]