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Proof step 56 from proof pathex-put-cyclic (previous step)

st[refs1 .last -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ refs1 = [], r = jvmref, refs1 .last = jvmref, r = refs1 .last, dups(refs1), r ∈ refs1, ∃ refs. dups(refs) ∧ refs .first = refs1 .last ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

User applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
refs1 = refs0 + r0 ', st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ refs1 = [], r = jvmref, r0 = jvmref, r = r0, dups(refs1), r ∈ refs1, ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r ' ,[refs, r, refs0] → [refs1, r0, refs0] ,T ,list-last ,references-olista ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (refs1, r0, refs0)]]