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Proof step 5 from proof valid-content-reduce (previous step)

∀ ino. ino ∈ files0 → valid-content(ino, files0) ⊦ valid-content(files1) ↔ (∀ ino, n. (ino ∈ files0 ∧ n ∈ files0[ino].content → n * VFS_PAGE_SIZE < files0[ino].size) → ino ∈ files1 ∧ n ∈ files1[ino].content → n * VFS_PAGE_SIZE < files1[ino].size)

User applied rule case distinction

And obtained the following new goals

Proof step 6:
valid-content(files1), ∀ ino. ino ∈ files0 → valid-content(ino, files0) ⊦ ∀ ino, n. (ino ∈ files0 ∧ n ∈ files0[ino].content → n * VFS_PAGE_SIZE < files0[ino].size) → ino ∈ files1 ∧ n ∈ files1[ino].content → n * VFS_PAGE_SIZE < files1[ino].size
Proof step 17:
∀ ino. ino ∈ files0 → valid-content(ino, files0), ∀ ino, n. (ino ∈ files0 ∧ n ∈ files0[ino].content → n * VFS_PAGE_SIZE < files0[ino].size) → ino ∈ files1 ∧ n ∈ files1[ino].content → n * VFS_PAGE_SIZE < files1[ino].size ⊦ valid-content(files1)

Rule argument

pos: right 1

Proof step 5 from proof valid-content-reduce (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information