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Proof step 19 from proof btree-mark-dirty (previous step)

(( r => mkznode(rp0, zbrar, false, false, height0) * bnode(r, zbrar, 0, height0, height0, height1 + 1, false, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh), nsize(height0, nstat), unmodified(adr, mkznode(rp0, zbrar, false, false, height0), iast), adr ∈ iast, adr ∈ alladrs, alladrs ⊆ dom iast, ∀ zh, r, rp0, zbrar, boolvar, height0, rp, adr, ri, iast, alladrs, nstat, P. zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ ((btree(rp, r, adr, height1, false, ri, iast, alladrs, alladrs, nstat) * P))(zh) ∧ r ∈ zh ∧ adr ∈ alladrs ∧ adr ∈ iast ∧ alladrs ⊆ dom iast ∧ (height1 = 0 → alladrs = ∅ ++ adr) → # alladrs = 0 ∨ alladrs = ∅ ∨ ((btree(rp, r, adr, height1, true, ri, iast, alladrs -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)]) ⊦ # alladrs = 0, alladrs = ∅, ∃ zbrar0, nused. nsize(nused, nstat) ∧ (( r => mkznode(rp0, zbrar0, false, true, nused) * bnode(r, zbrar0, 0, nused, nused, height1 + 1, true, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh[r, mkznode(rp0, zbrar, false, true, height0)])

User applied rule exists right

And obtained the following new goals

Proof step 20:
(( r => mkznode(rp0, zbrar, false, false, height0) * bnode(r, zbrar, 0, height0, height0, height1 + 1, false, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh), nsize(height0, nstat), unmodified(adr, mkznode(rp0, zbrar, false, false, height0), iast), adr ∈ alladrs, adr ∈ iast, alladrs ⊆ dom iast, ∀ zh, r, rp0, zbrar, boolvar, height0, rp, adr, ri, iast, alladrs, nstat, P. zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ ((btree(rp, r, adr, height1, false, ri, iast, alladrs, alladrs, nstat) * P))(zh) ∧ r ∈ zh ∧ adr ∈ alladrs ∧ adr ∈ iast ∧ alladrs ⊆ dom iast ∧ (height1 = 0 → alladrs = ∅ ++ adr) → # alladrs = 0 ∨ alladrs = ∅ ∨ ((btree(rp, r, adr, height1, true, ri, iast, alladrs -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)]) ⊦ # alladrs = 0, alladrs = ∅, nsize(height0, nstat) ∧ (( r => mkznode(rp0, zbrar, false, true, height0) * bnode(r, zbrar, 0, height0, height0, height1 + 1, true, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh[r, mkznode(rp0, zbrar, false, true, height0)])

Rule argument

pos: right 3 terms: zbrar, height0 abort: F discard: T computed: T

Additional information

Used terms: zbrar, height0