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Proof step 35 from proof validrefs-lastelem (previous step)

st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), refs0 .first = st[r1 -- mkfs(class1, ty2, fieldvar1) '] .refval, is_obj(str, r1, st), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0 + r ', ty0, st), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1, mkfs(class1, ty2, fieldvar1) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class1, ty2, fieldvar1) ']), validrefs(str, refs0, ty2, st) ⊦ r0 = jvmref, r1 = jvmref, refs0 = [], has_reffield(refs0 .last, st), ∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ refs0 .first = st[r1 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
refs0 = r2 + refs, st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), r2 = st[r1 -- mkfs(class1, ty2, fieldvar1) '] .refval, is_obj(str, r1, st), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0 + r ', ty0, st), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1, mkfs(class1, ty2, fieldvar1) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class1, ty2, fieldvar1) ']), validrefs(str, refs0, ty2, st) ⊦ r0 = jvmref, r1 = jvmref, refs0 = [], has_reffield(refs0 .last, st), ∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r2 = st[r1 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, r2, 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, r2, refs)]]