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Proof step 16 from proof validrefs-putbyte (previous step)

st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(refs0 .first), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, refs0, ty0, st), okbytearray(r, st), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, refs0 = [], ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ refs0 .first = st[r0 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st[r -- i ', byteval(by)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
refs0 = r1 + refs, st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, refs0, ty0, st), okbytearray(r, st), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, refs0 = [], ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r1 = st[r0 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st[r -- i ', byteval(by)])

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, 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 : (refs0, r1, refs)]]