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Proof step 58 from proof junkref-update-equiv (previous step)

validFields(r0, fis, st), is_valid_ref(str, r0, st), junkrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ junkref(str, r, update(r0, fis, st)), path∃(str, r, r0, st), _type ∈ fis

User applied rule structural induction

And obtained the following new goals

Proof step 13:
validFields(r0, fis, st), is_valid_ref(str, r0, st), junkrefs(str, r ' + [], st[r -- _type] .type, st) ⊦ junkref(str, r, update(r0, fis, st)), path∃(str, r, r0, st), _type ∈ fis
Proof step 57:
∀ r0, fis, st, str, r. validFields(r0, fis, st) ∧ is_valid_ref(str, r0, st) ∧ junkrefs(str, r ' + acc, st[r -- _type] .type, st) → junkref(str, r, update(r0, fis, st)) ∨ path∃(str, r, r0, st) ∨ _type ∈ fis, validFields(r0, fis, st), is_valid_ref(str, r0, st), junkrefs(str, r ' + (r1 + acc), st[r -- _type] .type, st) ⊦ junkref(str, r, update(r0, fis, st)), path∃(str, r, r0, st), _type ∈ fis

Rule argument

[VARWITHVARSEQSARG : refs0, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : references generated by [], +;])]]