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Proof step 15 from proof validrefs-has-null (previous step)

is_obj(str, r, st), jvmref ∈ acc, validrefs(str, (r ' + acc) + refs0, ty, st), st[r -- _type] .type ≤ ty, ∀ refs, str0, ty0, st0. refs ≠ [] → ¬ validrefs(str0, acc + refs, ty0, st0) ⊦ r = jvmref, refs0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st), jvmref ∈ acc, acc + refs0 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (acc + refs0) .first = st[r -- fs '] .refval ∧ validrefs(str, acc + refs0, fs .type, st)), st[r -- _type] .type ≤ ty, ∀ refs, str0, ty0, st0. refs ≠ [] → ¬ validrefs(str0, acc + refs, ty0, st0) ⊦ r = jvmref, refs0 = []

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, ty, acc + refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc + refs0, r, str)]]