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Proof step 15 from proof inv-format (previous step)

asynced0 ↔ asynced1, err = ESUCCESS, size = LEB_SIZE ⊦ ⟪icache_format#(; ; icache, err); if err = ESUCCESS then dcache_format#(; ; dcache, err); if err = ESUCCESS then pcache_format#(; ; pcache, err)⟫ ( err = ESUCCESS → true ∧ icache-cons(icache, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅) ∧ dcache-cons(dcache, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅) ∧ pcache-cons(pcache, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅) ∧ synced((∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], icache, pcache) ∧ (asynced1 → synced(∅, icache, pcache)) ∧ afs-cons((∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
⊦ ⟪icache_format#(; ; icache, err); if err = ESUCCESS then dcache_format#(; ; dcache, err); if err = ESUCCESS then pcache_format#(; ; pcache, err)⟫ ( err = ESUCCESS → icache-cons(icache, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅) ∧ dcache-cons(dcache, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅) ∧ pcache-cons(pcache, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅) ∧ synced((∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], icache, pcache) ∧ (asynced1 → synced(∅, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons((∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅); (s)