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Proof step 90 from proof exvalidrefs-maxlength (previous step)

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, validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st -- r), validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st), ∀ 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 = r1, r0 = r1, r = r0, r = jvmref, r0 = jvmref, has_reffield(r1, st), r ∈ refs1, dups(refs1), r1 ∈ refs1, r0 ∈ refs1, cyclic(str, r, st), junkref(str, r0, st), validrefs(str, r ' + r0 ' + refs1 + r1 ', st[r -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 86:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 89:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, 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, validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st -- r), validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st), ∀ 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 = r1, r0 = r1, r = r0, r = jvmref, r0 = jvmref, has_reffield(r1, st), r ∈ refs1, dups(refs1), r1 ∈ refs1, r0 ∈ refs1, cyclic(str, r, st), junkref(str, r0, st), r0 ' + refs1 + r1 ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs1 + r1 ') .first = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs1 + r1 ', fs .type, st))

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, r0 ' + refs1 + r1 ', r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, r0 ' + refs1 + r1 ', r, str)]]