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Proof step 9 from proof validref-class-rec (previous step)

fs = mkfs(class, ty0, fieldvar), st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), ∀ fs. ¬ fs ' ∈ instfields(st[r -- _type] .type .class) ∨ ¬ is_referencevalue(st[r -- fs ']) ∨ st[r -- fs '] .refval = jvmref ∨ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ ¬ junkref(str, st[r -- fs '] .refval, st) ⊦ r = jvmref, st[r -- fs '] .refval = jvmref, st[st[r -- fs '] .refval -- _type] .type ≤ ty0 ∧ validref(str, st[r -- fs '] .refval, ty0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ fs. ¬ fs ' ∈ instfields(st[r -- _type] .type .class) ∨ ¬ is_referencevalue(st[r -- fs ']) ∨ st[r -- fs '] .refval = jvmref ∨ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ ¬ junkref(str, st[r -- fs '] .refval, st) ⊦ r = jvmref, st[r -- mkfs(class, ty0, fieldvar) '] .refval = jvmref, st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∧ validref(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]