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Proof step 17 from proof junkref-put-nopathexplus-equiv (previous step)

junkrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ sk = _type, junkref(str, r, st[r0 -- sk, val]), path∃+(str, r, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ junkref(str, r, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[r -- _type] .type, st))
Proof step 16:
junkrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ sk = _type, ∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, (st[r0 -- sk, val][r -- _type]) .type, st[r0 -- sk, val]), path∃+(str, r, r0, st)

Rule argument

[speclemmaarg: , junkref(str, r, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[r -- _type] .type, st)) ,[st, r, str] → [st[r0 -- sk, val], r, str] ,F ,junkrefs , ,junkref-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- sk, val], r, str)]]