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Proof step 26 from proof synced-files-add-new-clean-inode (previous step)

pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), icache[ino, mkientry(false, inode)][ino0] = mkientry(boolvar0, inode0), ino0 ∈ files, ∀ ino0. ino0 ∈ files → (ino0 ∈ icache → ¬ icache[ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦ ino ∈ icache, (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ boolvar0) ∧ (datakey(ino0, n) ∈ pcache → ¬ boolvar)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 27:
icache[ino, mkientry(false, inode)][ino0] = mkientry(boolvar0, inode0), pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), ino0 = ino, ino0 ∈ files, ∀ ino0. ino0 ∈ files → (ino0 ∈ icache → ¬ icache[ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦ ino ∈ icache, (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ boolvar0) ∧ (datakey(ino0, n) ∈ pcache → ¬ boolvar)
Proof step 31:
icache[ino, mkientry(false, inode)][ino0] = mkientry(boolvar0, inode0), pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), ino0 ∈ files, ∀ ino0. ino0 ∈ files → (ino0 ∈ icache → ¬ icache[ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦ ino0 = ino, ino ∈ icache, (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ boolvar0) ∧ (datakey(ino0, n) ∈ pcache → ¬ boolvar)

Rule argument

fma: ino0 = ino

Additional information

Used formulas: ino0 = ino