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Proof step 75 from proof validrefs-putbyte-field (previous step)

refs1 .first = (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval, is_obj(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']), validrefs(str, refs1, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by, fieldvar, class, r, st, ty, str, refs0. # refs0 < # (r0 + refs1) → ( validrefs(str, refs0, ty, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st) ∨ validrefs(str, refs0, ty, st)) ⊦ refs1 = [], r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs1, r1, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs1, r1, refs)]]