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Proof step 7 from proof eq-io-readpage (previous step)

⟨afs_readpage#(p_inode, pageno0, dirs1, files1, asynced0; buf, err)⟩ (buf = buf0 ∧ err = err0), # buf = VFS_PAGE_SIZE, p_inode.ino ∈ files1 ⊦ ⟨fail#(; ; err)⟩ (buf = buf0 ∧ err = err0), ⟨if pageno0 ∈ files1[p_inode.ino].content then buf := files1[p_inode.ino].content[pageno0] else buf := zeropage; err := ESUCCESS⟩ (buf = buf0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
⟨afs_readpage#(p_inode, pageno0, dirs1, files1, asynced0; buf, err)⟩ (buf = buf0 ∧ err = err0), # buf = VFS_PAGE_SIZE, p_inode = mkinode(m, md, boolvar, m0, m1, m2), m ∈ files1 ⊦ ⟨fail#(; ; err)⟩ (buf = buf0 ∧ err = err0), ⟨if pageno0 ∈ files1[m].content then buf := files1[m].content[pageno0] else buf := zeropage; err := ESUCCESS⟩ (buf = buf0 ∧ err = err0)

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [p_inode, m, md, boolvar, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: p_inode, m, md, boolvar, m0, m1, m2