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Proof step 25 from proof validrefs-trans-01 (previous step)

st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, refs0 .last ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ' + refs0, ty1, st0) ∧ validrefs(str0, refs0 .last ' + refs, ty2, st0) → validrefs(str0, (r0 ' + refs0) + refs, ty1, st0) ⊦ refs0 = [], r = jvmref, ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, (st[r -- i '] .refval ' + refs0) + refs1, st[r -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
st[r -- i '] = refval(r0), validrefs(str, refs0 .last ' + refs1, ty0, st), is_array(str, r, st), i < st[r -- _length] .intval, validrefs(str, r0 ' + refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ' + refs0, ty1, st0) ∧ validrefs(str0, refs0 .last ' + refs, ty2, st0) → validrefs(str0, (r0 ' + refs0) + refs, ty1, st0) ⊦ r = jvmref, refs0 = [], validrefs(str, r0 ' + refs0 + refs1, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]