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

icache[ino, mkientry(false, inode)][ino0] = mkientry(boolvar1, inode2), pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), icache[ino] = mkientry(false, inode0), icache[ino0] = mkientry(boolvar0, inode1), ino0 ∈ dirs, ino ∈ icache, ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ boolvar1, ∀ 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), ∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty ⊦ ino0 = ino, (ino0 ∈ icache → ¬ boolvar0) ∧ (datakey(ino0, n) ∈ pcache → ¬ boolvar)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
icache[ino0] = mkientry(boolvar0, inode1), pcache[datakey(ino0, n)] = mkpentry(true, buf), icache[ino] = mkientry(false, inode0), datakey(ino0, n) ∈ pcache, ino0 ∈ dirs, ino ∈ icache, ino0 ∈ icache → ¬ boolvar0, ∀ 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), ∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty ⊦ ino0 = ino

Rule argument

Additional information

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