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Proof step 14 from proof synced-dirs-add-new-clean-inode (previous step)

icache[ino0] = mkientry(boolvar0, inode0), pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), icache[ino, mkientry(false, inode)][ino0] = mkientry(boolvar1, inode1), datakey(ino0, n) ∈ pcache, ino0 ∈ dirs, ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ boolvar1, ino ∈ dirs → (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty, ∀ ino0. ino0 ∈ dirs → (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ icache[ino, mkientry(false, inode)][ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦ ino ∈ icache, (ino0 ∈ icache → ¬ boolvar0) ∧ ¬ boolvar

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: ¬ boolvar

Additional information

Used simplifier rules: ⊦ ino ∈ icache ∧ ¬ ino0 ∈ icache → icache[ino0, ie][ino] = icache[ino]; (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws) Used formulas: ¬ boolvar