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Proof step 42 from proof exvalidrefs-maxlength (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(refs .first), is_obj(r, st), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty), st[refs .first -- _type] .type ≤ ty, dups(refs), validrefs(str, refs, st[refs .first -- _type] .type, st -- r), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r = refs .first, r = jvmref, refs .first = jvmref, cyclic(str, r, st), junkref(str, refs .first, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 41:
refs = r0 + refs0 ∧ refs ≠ [], st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_obj(r, st), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty), st[r0 -- _type] .type ≤ ty, dups(refs), validrefs(str, refs, st[r0 -- _type] .type, st -- r), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r = r0, r = jvmref, r0 = jvmref, cyclic(str, r, st), junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs, r0, refs0] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ dups([])], [CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs, r0, refs0)]]