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Proof step 3 from proof link-mod-dir-meta (previous step)

m ∈ dirs ⊦ links(ino, dirs[m, dirs[m].meta:= md]) = links(ino, dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 5:
m ∈ dirs ⊦ ∀ alink. alink ∈ links(ino, dirs[m, dirs[m].meta:= md]) ↔ alink ∈ links(ino, dirs)

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [links(ino, dirs), links(ino, dirs[m, dirs[m].meta:= md])] flags: <all paths>

Additional information

Used terms: links(ino, dirs), links(ino, dirs[m, dirs[m].meta:= md])