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Proof step 38 from proof abs-nlinks-h (previous step)

tree[p0] = dnode(md, sdt), tree[p0 + str '] = fnode(⌜ino1⌝ ), ((m0 => mkdir(# entries, md, m1, m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p0, m0)) )(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ sdt, p0 ∈ tree, ino1 ∈ files, ino0 ∈ dirs, str ∈ entries, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ alink. ¬ alink.pino ∈ dirs ∨ ¬ alink.name ∈ dirs[alink.pino].entries ∨ ino1 ≠ dirs[alink.pino].entries[alink.name], entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦

User applied rule all left

And obtained the following new goals

Proof step 39:
tree[p0 + str '] = fnode(⌜ino1⌝ ), tree[p0] = dnode(md, sdt), ((m0 => mkdir(# entries, md, m1, m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p0, m0)) )(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ entries, ino0 ∈ dirs, ino1 ∈ files, p0 ∈ tree, str ∈ sdt, ∀ alink. ¬ alink.pino ∈ dirs ∨ ¬ alink.name ∈ dirs[alink.pino].entries ∨ ino1 ≠ dirs[alink.pino].entries[alink.name], ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, entries[str] ∈ dirs ∨ entries[str] ∈ files, ¬ mklink(m0, str).pino ∈ dirs ∨ ¬ mklink(m0, str).name ∈ dirs[mklink(m0, str).pino].entries ∨ ino1 ≠ dirs[mklink(m0, str).pino].entries[mklink(m0, str).name] ⊦

Rule argument

pos: left 12 terms: mklink(m0, str) abort: F discard: F computed: F

Additional information

Used terms: mklink(m0, str)