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Proof step 10 from proof abs-acyclic (previous step)

entries[str] = ROOT_INO, dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), abs(tree, ROOT_INO) = _∃(λ ino1. abs|(tree, ROOT_INO, p, ino1) * abs(tree[p], ino1)), tree[p].dir?, abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), ino ∈ dirs, str ∈ entries ⊦

User applied rule expand left

And obtained the following new goals

Proof step 11:
abs(tree, ROOT_INO)(dirs) ↔ (_∃(λ ino1. abs|(tree, ROOT_INO, p, ino1) * abs(tree[p], ino1)))(dirs), dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), entries[str] = ROOT_INO, tree[p].dir?, abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), str ∈ entries, ino ∈ dirs ⊦

Rule argument

pos: left 3 terms: dirs abort: F discard: T computed: T

Additional information

Used terms: dirs