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Proof step 6 from proof links-inc-nsubdirs (previous step)

p_ino ∈ dirs, alink.pino ∈ dirs ⊦ alink.name ∈ (alink.pino = p_ino ⊃ mkdir(m0, md, n0, n1 + 1, entries);dirs[alink.pino]).entries ∧ ino = (alink.pino = p_ino ⊃ mkdir(m0, md, n0, n1 + 1, entries);dirs[alink.pino]).entries[alink.name] ↔ alink.name ∈ (alink.pino = p_ino ⊃ mkdir(m0, md, n0, n1, entries);dirs[alink.pino]).entries ∧ ino = (alink.pino = p_ino ⊃ mkdir(m0, md, n0, n1, entries);dirs[alink.pino]).entries[alink.name]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
alink = mklink(m, str), m ∈ dirs, p_ino ∈ dirs ⊦ str ∈ (m = p_ino ⊃ mkdir(m0, md, n0, n1 + 1, entries);dirs[m]).entries ∧ ino = (m = p_ino ⊃ mkdir(m0, md, n0, n1 + 1, entries);dirs[m]).entries[str] ↔ str ∈ (m = p_ino ⊃ mkdir(m0, md, n0, n1, entries);dirs[m]).entries ∧ ino = (m = p_ino ⊃ mkdir(m0, md, n0, n1, entries);dirs[m]).entries[str]

Rule argument

spec: alink name: elim seq: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str) subst: [alink, m, str] → [alink, m, str]

Additional information

Used simplifier rules: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str); (elim) Used terms: alink, m, str