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Proof step 24 from proof validrefs-addarray (previous step)

st[r0 -- i '] = refval(r2), validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, addarray(r, ty0, vals, st)), i < st[r0 -- _length] .intval, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, newref(r, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, ∀ str0, ty1, r1, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r1, ty2, vals0, st0)) ∧ newref(r1, st0) → r1 = jvmref ∨ r1 = r2 ∨ r1 ∈ refs ∨ validrefs(str0, r2 ' + refs, ty1, st0) ⊦ r = r2, r0 = jvmref, r = r0, r = jvmref, r ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r2 = st[r0 -- i0 '] .refval ∧ validrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st)

User applied rule exists right

And obtained the following new goals

Proof step 23:
st[r0 -- i '] = refval(r2), validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, addarray(r, ty0, vals, st)), i < st[r0 -- _length] .intval, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, newref(r, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, ∀ str0, ty1, r1, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r1, ty2, vals0, st0)) ∧ newref(r1, st0) → r1 = jvmref ∨ r1 = r2 ∨ r1 ∈ refs ∨ validrefs(str0, r2 ' + refs, ty1, st0) ⊦ r = r2, r0 = jvmref, r = r0, r = jvmref, r ∈ refs, ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r2 = st[r0 -- i '] .refval ∧ validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st)

Rule argument

[EXRARG : pos: right 6, [extquanttermlist: (i)abort:F, discard:T, computed:T]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i)]]