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Proof step 45 from proof validrefs-putbyte (previous step)

st[r0 -- i0 '] = refval(r1), i0 < st[r0 -- _length] .intval, is_array(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i0, okbytearray(r, st), is_array(str, r0, st), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + (r1 + refs)) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i ', byteval(by)][r0 -- i1 ']) ∧ r1 = (st[r -- i ', byteval(by)][r0 -- i1 ']) .refval ∧ validrefs(str, (st[r -- i ', byteval(by)][r0 -- i1 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)])

User applied rule exists right

And obtained the following new goals

Proof step 44:
st[r0 -- i0 '] = refval(r1), i0 < st[r0 -- _length] .intval, is_array(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i0, okbytearray(r, st), is_array(str, r0, st), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + (r1 + refs)) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i ', byteval(by)][r0 -- i0 ']) ∧ r1 = (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval ∧ validrefs(str, (st[r -- i ', byteval(by)][r0 -- i0 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', byteval(by)])

Rule argument

[EXRARG : pos: right 2, [extquanttermlist: (i0)abort:F, discard:T, computed:F]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0)]]