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Proof step 111 from proof btree-clean-fwd-strong (previous step)

# asar0 = (n0 + 1) + n, # zbrar = BRANCH_SIZE, # asar1 = # asar0, # asar2 = # asar0, # asar = # asar0, # zbrar0 = BRANCH_SIZE, zbrar[n] = mkzbranch(key0, adr1, r3), zbrar0[n] = mkzbranch(key0, adr1, r4), asar[n] = asar0[n], asar1[n] = asar2[n], union(asar, 0, # asar0) = union(asar0, 0, # asar0), union(asar1, 0, # asar0) = union(asar2, 0, # asar0), ((btree(r, r3, adr1, height0, false, key-range(zbrar, n, # asar0, ri1), iast1, asar2[n], asar2[n], ok) * P))(zh3), ((btree(r2, r4, adr1, height, false, key-range(zbrar0, n, # asar0, ri0), iast0, asar0[n], asar0[n], ok) * P2))(zh), n0 + n < BRANCH_SIZE, n < BRANCH_SIZE, ((r2 => mkznode(rp0, zbrar0, false, false, # asar0)))(zh5), ((r => mkznode(rp1, zbrar, false, false, # asar0)))(zh4), disj(asar, 0, # asar0), disj(asar0, 0, # asar0), disj(asar1, 0, # asar0), disj(asar2, 0, # asar0), nsize(# asar0, nstat), sorted(zbrar0, 0, n0 + n), sorted(zbrar, 0, n0 + n), unmodified(adr, mkznode(rp1, zbrar, false, false, # asar0), iast1), unmodified(adr, mkznode(rp0, zbrar0, false, false, # asar0), iast0), adr ∈ iast1, adr ∈ iast0, iast0 ⊆ iast1, asar2[n] ⊆ dom iast1, asar0[n] ⊆ dom iast0, zh5 ⊥ zh, zh4 ⊥ zh3, (r0 = null ⊃ P0(zh0);r2 = r0 ∧ zh5 ∪ zh = zh0), (r1 = null ⊃ P1(zh1);r = r1 ∧ zh4 ∪ zh3 = zh1), ∀ n1. ¬ n0 + n < n1 → asar0[n1] ⊆ dom iast0, ∀ n1. ¬ n0 + n < n1 → asar2[n1] ⊆ dom iast1, ∀ 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 ⊦ asar0[n] = asar2[n], union(asar0, 0, # asar0) = union(asar2, 0, # asar0), adr ∈ union(asar2, 0, # asar0), adr ∈ union(asar0, 0, # asar0)

User applied rule all left

And closed the goal!

Rule argument

pos: left 39 terms: r, r3, adr1, height0, key-range(zbrar, n, # asar0, ri1), iast1, asar2[n], ok, P, zh3, r2, r4, key-range(zbrar0, n, # asar0, ri0), iast0, asar0[n], P2, zh abort: F discard: T computed: F

Additional information

Used terms: r, r3, adr1, height0, key-range(zbrar, n, # asar0, ri1), iast1, asar2[n], ok, P, zh3, r2, r4, key-range(zbrar0, n, # asar0, ri0), iast0, asar0[n], P2, zh