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Proof step 15 from proof validrefs-levelsubset (previous step)

st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str, r, st), ∀ str, ty0, st, str0. validrefs(str, acc, ty0, st) ∧ level⊆(str, str0) → validrefs(str0, acc, ty0, st), acc = [] ∨ mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']) ∧ acc .first = st[r -- mkfs(class, ty, fieldvar) '] .refval ∧ validrefs(str, acc, ty, st) ⊦ r = jvmref, validrefs(str0, r ' + acc, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 14:
is_obj(str0, r, st) ∧ st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str, r, st), ∀ str, ty0, st, str0. validrefs(str, acc, ty0, st) ∧ level⊆(str, str0) → validrefs(str0, acc, ty0, st), acc = [] ∨ mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']) ∧ acc .first = st[r -- mkfs(class, ty, fieldvar) '] .refval ∧ validrefs(str, acc, ty, st) ⊦ r = jvmref, acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str0, acc, fs .type, st))

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, ty0, acc, r, str0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj(str, r, st) ∧ level⊆(str, str0) → (¬ is_obj(str0, r, st) ↔ false)])], [EXTRATERMS : (st, ty0, acc, r, str0)]]