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Proof step 6 from proof link-mod-dir-meta (previous step)

m ∈ dirs, alink.pino ∈ dirs ⊦ alink.name ∈ (alink.pino = m ⊃ dirs[alink.pino].meta:= md;dirs[alink.pino]).entries ∧ ino = (alink.pino = m ⊃ dirs[alink.pino].meta:= md;dirs[alink.pino]).entries[alink.name] ↔ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
alink = mklink(m0, str), m0 ∈ dirs, m ∈ dirs ⊦ str ∈ (m0 = m ⊃ dirs[m0].meta:= md;dirs[m0]).entries ∧ ino = (m0 = m ⊃ dirs[m0].meta:= md;dirs[m0]).entries[str] ↔ str ∈ dirs[m0].entries ∧ ino = dirs[m0].entries[str]

Rule argument

spec: alink name: elim seq: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str) subst: [alink, m, str] → [alink, m0, str]

Additional information

Used simplifier rules: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str); (elim) Used terms: alink, m0, str