[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 9 from proof btree-inv-clean-commit (previous step)

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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
zh[rp] = mkznode(r, zbrar, boolvar, boolvar0, m), ((btree(null, null, adr, height, false, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, rp, adr, height, false, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, null, adr, height, false, ri, nodes(istore0), as, alladrs, ok) * true))(zh), refsize-cons(istore, as), refsize-cons(istore0, as), adr ∈ istore, alladrs ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, as ⊆ dom nodes(istore0), 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))

Rule argument

Additional information

Used simplifier rules: btree-crash: ⊦ (( btree (null, null, adr, height, false, fi, iast0, as, alladrs, ok) * true) )(zh0) → (( btree (null, null, adr, height, false, fi, iast0, as, alladrs, ok) * true) )(zh1);%btree-clean-fwd: ⊦ (( 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;%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast;%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]% ⊦ istore ⊑ istore0 → nodes(istore) ⊆ nodes(istore0); (ss)