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Proof step 11 from proof validref-class-rec-better (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st) ⊦ ¬ (∃ 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 ∨ ¬ validref(str, st[r -- fs '] .refval, fs .type, st))) ↔ st[r -- _type] .type ≤ ty ∧ (∀ 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 ∧ validref(str, st[r -- fs '] .refval, fs .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
st[r -- _type] .type ≤ ty, is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), ∀ 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 ∧ validref(str, st[r -- fs '] .refval, fs .type, st) ⊦ st[r -- fs '] .refval = jvmref, st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ validref(str, st[r -- fs '] .refval, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]