[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 17 from proof btree-clean-fwd-strong (previous step)

(( r => mkznode(rp1, zbrar, false, false, nused) * bnode(r, zbrar, 0, nused, nused, height1, false, ri1, iast1, alladrs1 -- adr, alladrs1 -- adr) * P1) )(zh), (( r2 => mkznode(rp0, zbrar0, false, false, nused) * bnode(r2, zbrar0, 0, nused, nused, height + 1, false, ri0, iast0, alladrs0 -- adr, alladrs0 -- adr) * P0) )(zh2), nsize(nused, nstat), unmodified(adr, mkznode(rp1, zbrar, false, false, nused), iast1), unmodified(adr, mkznode(rp0, zbrar0, false, false, nused), iast0), adr ∈ iast1, adr ∈ alladrs1, adr ∈ iast0, adr ∈ alladrs0, alladrs1 ⊆ dom iast1, alladrs0 ⊆ dom iast0, iast0 ⊆ iast1, (r0 = null ⊃ P0(zh0);r2 = r0 ∧ zh2 = zh0), (r1 = null ⊃ P1(zh1);r = r1 ∧ zh = zh1), ∀ rp1, r1, adr, height1, ri1, iast1, alladrs1, nstat, P1, zh1, rp0, r0, ri0, iast0, alladrs0, P0, zh0. ((btree(rp1, r1, adr, height1, false, ri1, iast1, alladrs1, alladrs1, nstat) * P1))(zh1) ∧ ((btree(rp0, r0, adr, height, false, ri0, iast0, alladrs0, alladrs0, nstat) * P0))(zh0) ∧ alladrs1 ⊆ dom iast1 ∧ alladrs0 ⊆ dom iast0 ∧ iast0 ⊆ iast1 → height = height1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1 ⊦ # alladrs1 = 0, # alladrs0 = 0, alladrs0 = ∅, alladrs1 = ∅, height1 = 0, height + 1 = height1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1

User applied rule constructor cut

And obtained the following new goals

Proof step 18:
height1 = height0 +1, (( r2 => mkznode(rp0, zbrar0, false, false, nused) * bnode(r2, zbrar0, 0, nused, nused, height + 1, false, ri0, iast0, alladrs0 -- adr, alladrs0 -- adr) * P0) )(zh2), (( r => mkznode(rp1, zbrar, false, false, nused) * bnode(r, zbrar, 0, nused, nused, height1, false, ri1, iast1, alladrs1 -- adr, alladrs1 -- adr) * P1) )(zh), nsize(nused, nstat), unmodified(adr, mkznode(rp0, zbrar0, false, false, nused), iast0), unmodified(adr, mkznode(rp1, zbrar, false, false, nused), iast1), adr ∈ alladrs0, adr ∈ iast0, adr ∈ alladrs1, adr ∈ iast1, iast0 ⊆ iast1, alladrs0 ⊆ dom iast0, alladrs1 ⊆ dom iast1, (r1 = null ⊃ P1(zh1);r = r1 ∧ zh = zh1), (r0 = null ⊃ P0(zh0);r2 = r0 ∧ zh2 = zh0), ∀ rp1, r1, adr, height1, ri1, iast1, alladrs1, nstat, P1, zh1, rp0, r0, ri0, iast0, alladrs0, P0, zh0. ((btree(rp1, r1, adr, height1, false, ri1, iast1, alladrs1, alladrs1, nstat) * P1))(zh1) ∧ ((btree(rp0, r0, adr, height, false, ri0, iast0, alladrs0, alladrs0, nstat) * P0))(zh0) ∧ alladrs1 ⊆ dom iast1 ∧ alladrs0 ⊆ dom iast0 ∧ iast0 ⊆ iast1 → height = height1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1 ⊦ # alladrs0 = 0, # alladrs1 = 0, alladrs0 = ∅, alladrs1 = ∅, height1 = 0, height + 1 = height1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1

Rule argument

var: height1

Additional information

Used simplifier rules: nat freely generated by 0, +1;;