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Proof step 6 from proof inv-close (previous step)

err0 = err1, root.dir?, fids-cons(root, fs, ofh), pre-close(fd, err, user, root, fs, ofh) ⊦ ⟪if err = ESUCCESS then let fid = ofh[fd].fid in {ofh := ofh -- fd; if ¬ fid ∈ ofh.fids ∧ ¬ fid ∈ root.fids then fs := fs -- fid}⟫ fids-cons(root, fs, ofh)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Proof step 7:
err = ESUCCESS, err0 = err1, root.dir?, fids-cons(root, fs, ofh), pre-close(fd, err, user, root, fs, ofh) ⊦ ⟪let fid = ofh[fd].fid in {ofh := ofh -- fd; if ¬ fid ∈ ofh.fids ∧ ¬ fid ∈ root.fids then fs := fs -- fid}⟫ fids-cons(root, fs, ofh)
Proof step 57:
err0 = err1, root.dir?, fids-cons(root, fs, ofh), pre-close(fd, err, user, root, fs, ofh) ⊦ ⟪skip⟫ fids-cons(root, fs, ofh), err = ESUCCESS

Rule argument

pos: right 1

Proof step 6 from proof inv-close (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

Additional information