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Proof step 22 from proof validrefs-delcycle-01 (previous step)

(acc + r ') .first = st[r0 -- fs '] .refval, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, fs ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- fs ']), validrefs(str, acc + r ' + refs0 + r ' + refs1, fs .type, st), ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 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 21:
is_obj(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, (acc + r ') .first = st[r0 -- fs '] .refval, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, fs ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- fs ']), validrefs(str, acc + r ' + refs0 + r ' + refs1, fs .type, st), ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, acc + r ' + refs1 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ (acc + r ' + refs1) .first = st[r0 -- fs '] .refval ∧ validrefs(str, acc + r ' + refs1, fs .type, st))

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, ty, acc + r ' + refs1, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc + r ' + refs1, r0, str)]]