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Proof step 3 from proof ofh-fids-new (previous step)

⊦ ofh[fd, fh].fids = ofh.fids ++ fh.fid, fd ∈ ofh

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ fids = fids0 ↔ (∀ fid. fid ∈ fids ↔ fid ∈ fids0)
Proof step 5:
⊦ fd ∈ ofh, ∀ fid. fid ∈ ofh[fd, fh].fids ↔ fid ∈ ofh.fids ++ fh.fid

Rule argument

spec: set-basic, inst: fidset name: Extension seq: ⊦ fids = fids0 ↔ (∀ fid. fid ∈ fids ↔ fid ∈ fids0) subst: [fids0, fids] → [ofh.fids ++ fh.fid, ofh[fd, fh].fids] flags: <all paths>

Additional information

Used terms: ofh.fids ++ fh.fid, ofh[fd, fh].fids