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Proof step 40 from proof validrefs-addarray-junkref (previous step)

newref(r, st), validrefs(str, r1 ' + r2 ' + refs, ty0, addarray(r, ty, vals, st)), ∀ str0, ty1, r0, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r0, ty2, vals0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r = r1, r = jvmref, junkref(str, r1, st), r ≠ r2 ∧ ¬ r ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 39:
r1 ≠ jvmref, newref(r, st), validrefs(str, r1 ' + r2 ' + refs, ty0, addarray(r, ty, vals, st)), ∀ str0, ty1, r0, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r0, ty2, vals0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r = r1, r = jvmref, junkref(str, r1, st), r ≠ r2 ∧ ¬ r ∈ refs

Rule argument

[crewrite-arg: validrefs-null , F , [st, ty, refs, r, str] → [addarray(r, ty, vals, st), ty0, r2 ' + refs, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (addarray(r, ty, vals, st), ty0, r2 ' + refs, r1, str)]]