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Proof step 18 from proof links-del-entry (previous step)

ino0 ∈ dirs, str ∈ entries, alink.pino ∈ dirs ⊦ alink.name ∈ (alink.pino = ino0 ⊃ mkdir(m, md, n0, n1, entries -- str);dirs[alink.pino]).entries ∧ ino = (alink.pino = ino0 ⊃ mkdir(m, md, n0, n1, entries -- str);dirs[alink.pino]).entries[alink.name] ↔ alink.name ∈ (alink.pino = ino0 ⊃ mkdir(m, md, n0, n1, entries);dirs[alink.pino]).entries ∧ ino = (alink.pino = ino0 ⊃ mkdir(m, md, n0, n1, entries);dirs[alink.pino]).entries[alink.name], entries[str] = ino

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
alink = mklink(m0, str0), m0 ∈ dirs, str ∈ entries, ino0 ∈ dirs ⊦ str0 ∈ (m0 = ino0 ⊃ mkdir(m, md, n0, n1, entries -- str);dirs[m0]).entries ∧ ino = (m0 = ino0 ⊃ mkdir(m, md, n0, n1, entries -- str);dirs[m0]).entries[str0] ↔ str0 ∈ (m0 = ino0 ⊃ mkdir(m, md, n0, n1, entries);dirs[m0]).entries ∧ ino = (m0 = ino0 ⊃ mkdir(m, md, n0, n1, entries);dirs[m0]).entries[str0], entries[str] = ino

Rule argument

spec: alink name: elim seq: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str) subst: [alink, m, str] → [alink, m0, str0]

Additional information

Used simplifier rules: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str); (elim) Used terms: alink, m0, str0