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Proof step 138 from proof exvalidrefs-03 (previous step)

st[r -- _type] .type ≤ mkclasstype(class), is_obj(str, r, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), ty ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ mkclasstype(class), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, cyclic(str, r, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, mkfs(class0, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class0, ty, fieldvar) ']) ∧ st[r -- mkfs(class0, ty, fieldvar) '] .refval ≠ jvmref ∧ (¬ st[st[r -- mkfs(class0, ty, fieldvar) '] .refval -- _type] .type ≤ ty ∨ junkref(str, st[r -- mkfs(class0, ty, fieldvar) '] .refval, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ fs ' ∈ instfields(class) ∧ ty ≤ mkclasstype(class) ∧ is_classtype(ty) → fs ' ∈ instfields(ty .class)
Proof step 137:
mkfs(class0, ty, fieldvar) ' ∈ instfields(class) ∧ st[r -- _type] .type ≤ mkclasstype(class) ∧ is_classtype(st[r -- _type] .type), st[r -- _type] .type ≤ mkclasstype(class), is_obj(str, r, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), ty ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ mkclasstype(class), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, cyclic(str, r, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, true ∧ is_referencevalue(st[r -- mkfs(class0, ty, fieldvar) ']) ∧ st[r -- mkfs(class0, ty, fieldvar) '] .refval ≠ jvmref ∧ (¬ st[st[r -- mkfs(class0, ty, fieldvar) '] .refval -- _type] .type ≤ ty ∨ junkref(str, st[r -- mkfs(class0, ty, fieldvar) '] .refval, st))

Rule argument

[speclemmaarg: , fs ' ∈ instfields(class) ∧ ty ≤ mkclasstype(class) ∧ is_classtype(ty) → fs ' ∈ instfields(ty .class) ,[fs, class, ty] → [mkfs(class0, ty, fieldvar), class, st[r -- _type] .type] ,F ,addfuns , ,instfields-subclass-in ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_classtype (st[r -- _type] .type) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (mkfs(class0, ty, fieldvar), class, st[r -- _type] .type)]]