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Proof step 62 from proof junkref-update-equiv (previous step)

junkref(str, r, st), validFields(r0, fis, st), is_valid_ref(str, r0, st) ⊦ junkref(str, r, update(r0, fis, st)), path∃(str, r, r0, st), _type ∈ fis

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ junkref(str, r, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[r -- _type] .type, st))
Proof step 61:
∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[r -- _type] .type, st), validFields(r0, fis, st), is_valid_ref(str, r0, st) ⊦ junkref(str, r, update(r0, fis, st)), path∃(str, r, r0, st), _type ∈ fis

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str)]]