[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 6 from proof fid-in-fs (previous step)

ofh[fd] = mkfh(fid, mode, m), fd ∈ ofh, ∀ fid. fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh.fids ⊦ fid ∈ fs, fid ∈ root.fids, fid ∈ ofh.fids

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ fid ∈ ofh.fids ↔ (∃ n. n ∈ ofh ∧ ofh[n].fid = fid)
Proof step 8:
ofh[fd] = mkfh(fid, mode, m), fd ∈ ofh, ∀ fid. fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh.fids ⊦ fid ∈ root.fids, fid ∈ fs, ∃ n. n ∈ ofh ∧ ofh[n].fid = fid

Rule argument

spec: posix-base name: ofh-fids seq: ⊦ fid ∈ ofh.fids ↔ (∃ n. n ∈ ofh ∧ ofh[n].fid = fid) subst: [ofh, fid] → [ofh, fid] flags: <all paths>

Additional information

Used terms: ofh, fid