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Proof step 7 from proof links-del-entry (previous step)

str ∈ entries, ino0 ∈ dirs ⊦ links(entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries -- str)]) = links(entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 9:
ino0 ∈ dirs, str ∈ entries ⊦ ∀ alink. alink ∈ links(entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries -- str)]) ↔ alink ∈ links(entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str)

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [ links (entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str), links (entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries -- str)])] flags: <all paths>

Additional information

Used terms: links(entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str), links(entries[str], dirs[ino0, mkdir(m, md, n0, n1, entries -- str)])