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Proof step 9 from proof validref-forward-array (previous step)

is_array(str, r, st0) ∧ st0[r -- _type] .type ≤ mkarraytype(ty), st0[r -- i '] = refval(r0), st0[r -- _type] .type = mkarraytype(ty0), is_array(str, r, st0), ∀ i. ¬ ( 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st0[r -- i ']) ∧ st0[r -- i '] .refval ≠ jvmref ∧ ( ¬ st0[st0[r -- i '] .refval -- _type] .type ≤ st0[r -- _type] .type .type ∨ ¬ validref(str, st0[r -- i '] .refval, st0[r -- _type] .type .type, st0))), i < st0[r -- _length] .intval, 0 ≤ i, 0 < st0[r -- _length] .intval, ty0 ≤ ty ⊦ r = jvmref, validref(str, r0, ty, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
st0[r -- _type] .type = mkarraytype(ty0), st0[r -- i '] = refval(r0), 0 < st0[r -- _length] .intval, 0 ≤ i, i < st0[r -- _length] .intval, is_array(str, r, st0), ty0 ≤ ty, ∀ i0. i0 < 0 ∨ st0[r -- _length] .intval ≤ i0 ∨ ¬ is_referencevalue(st0[r -- i0 ']) ∨ st0[r -- i0 '] .refval = jvmref ∨ st0[st0[r -- i0 '] .refval -- _type] .type ≤ ty0 ∧ validref(str, st0[r -- i0 '] .refval, ty0, st0) ⊦ r = jvmref, validref(str, r0, ty, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty])]]