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Proof step 31 from proof validrefs-put-badarrayfield (previous step)

st[r -- i '] = refval(r1), st[r -- _type] .type = mkarraytype(ty0), validrefs(str, r1 ' + refs, ty0, st[r0 -- fs ', val]), i < st[r -- _length] .intval, mkarraytype(ty0) ≤ ty, is_array(str, r, st), is_arraytype(st[r0 -- _type] .type), junkref(str, r1, st), 0 < st[r -- _length] .intval, 0 ≤ i ⊦ r = jvmref, fs ' = _length, fs ' = _type, validrefs(str, r1 ' + refs, ty0, st), r ∈ (r1 ' + refs) .butlast, dups((r1 ' + refs) .butlast), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- i0 '] .refval -- _type] .type ≤ ty0 ∨ junkref(str, st[r -- i0 '] .refval, st))

User applied rule exists right

And obtained the following new goals

Proof step 30:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []

Rule argument

[EXRARG : pos: right 7, [extquanttermlist: (i)abort:F, discard:T, computed:T]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ¬ junkref(str, jvmref, st)])], [EXTRATERMS : (i)]]