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Proof step 12 from proof at-pcache-overwrite-other (previous step)

files[ino] = mkfile(m, md, m0, content), n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]) ⊦ ino = key0.ino, n ∈ content ⊕ mkcontent(ino, pcache) ∧ (content ⊕ mkcontent(ino, pcache[key0, pe]))[n] = (content ⊕ mkcontent(ino, pcache))[n]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 13:
files[ino] = mkfile(m, md, m0, content), n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]), n ∈ content ⊕ mkcontent(ino, pcache) ⊦ ino = key0.ino, n ∈ content ⊕ mkcontent(ino, pcache) ∧ (content ⊕ mkcontent(ino, pcache[key0, pe]))[n] = (content ⊕ mkcontent(ino, pcache))[n]

Rule argument

fma: n ∈ content ⊕ mkcontent(ino, pcache)

Additional information

Used simplifier rules: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)% ⊦ datakey(m, m0).ino = m; (s) Used formulas: n ∈ content ⊕ mkcontent(ino, pcache)