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Proof step 5 from proof links-modmeta (previous step)

dirs[ino] = mkdir(m0, md0, n1, n2, entries), ino ∈ dirs ⊦ ∀ alink. alink ∈ links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) ↔ alink ∈ links(ino0, dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
dirs[ino] = mkdir(m0, md0, n1, n2, entries), ino ∈ dirs, alink.pino ∈ dirs ⊦ alink.name ∈ (alink.pino = ino ⊃ mkdir(m, md, n, n0, entries);dirs[alink.pino]).entries ∧ ino0 = (alink.pino = ino ⊃ mkdir(m, md, n, n0, entries);dirs[alink.pino]).entries[alink.name] ↔ alink.name ∈ dirs[alink.pino].entries ∧ ino0 = dirs[alink.pino].entries[alink.name]

Rule argument

Additional information

Used simplifier rules: links: ⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name];% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)