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Proof step 47 from proof validrefs-delcycle (previous step)

refs1 .last = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0 + r ' + refs1, ty, st), ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ refs1 = [], validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 46:
r0 ≠ jvmref, refs1 .last = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0 + r ' + refs1, ty, st), ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ refs1 = [], validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

Rule argument

[crewrite-arg: validrefs-null , F , [st, ty, refs, r, str] → [st, ty, acc + r ' + refs0 + r ' + refs1, r0, str] ]

Additional information

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