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Proof step 71 from proof validrefs-subset-equiv (previous step)

st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, r -- i ' ∈ st, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st0), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, st ⊆ st0, is_array(str, r, st), 0 ≤ i, r ∈ st, r -- _length ∈ st, r -- _type ∈ st, junkref(str, r0, st), ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), ∃ 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 ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i0 '] .refval, st))

User applied rule exists right

And obtained the following new goals

Rule argument

[EXRARG : pos: right 3, [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)]]