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Proof step 14 from proof validrefs-subset-equiv (previous step)

r -- _type ∈ st ∧ st ⊆ st0, st[r -- _type] .type ≤ ty, is_valid_ref(str, r, st), st ⊆ st0, is_obj(str, r, st0), refs = [] ∨ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- mkfs(class, ty0, fieldvar) ']) ∧ refs .first = st0[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(str, refs, ty0, st0), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, validrefs(str, r ' + refs, ty, st), junkref(str, r, st), is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
st ⊆ st0, is_obj(str, r, st0), r -- _type ∈ st, st[r -- _type] .type ≤ ty, is_array(str, r, st), r ∈ st, refs = [] ∨ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- mkfs(class, ty0, fieldvar) ']) ∧ refs .first = st0[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(str, refs, ty0, st0), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, validrefs(str, r ' + refs, ty, st), junkref(str, r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)], [CSIMPSEQ : ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))])]]