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Proof step 10 from proof validref-forward (previous step)

is_obj(str, r, st0), st0[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), is_reftype(ty), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), st0[r -- _type] .type ≤ mkclasstype(class), is_valid_ref(str, r, st0) ⊦ r = jvmref, r0 = jvmref, ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st0[r -- fs ']) ∨ ¬ st0[st0[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st0[r -- fs '] .refval, st0)), st0[r0 -- _type] .type ≤ ty ∧ ¬ junkref(str, r0, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
st0[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), is_obj(str, r, st0), is_reftype(ty), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), st0[r -- _type] .type ≤ mkclasstype(class) ⊦ r = jvmref, r0 = jvmref, ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st0[r -- fs ']) ∨ ¬ st0[st0[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st0[r -- fs '] .refval, st0)), st0[r0 -- _type] .type ≤ ty ∧ ¬ junkref(str, r0, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)])]]