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Proof step 40 from proof validrefs-junkrefs-01 (previous step)

st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, (r0 ' + refs1) + refs0, st[r -- _type] .type .type, st), ∀ str0, refs2, ty0, st0. junkrefs(str0, (r0 ' + refs1) + refs2, ty0, st0) → junkrefs(str0, r0 ' + refs1, ty0, st0) ∨ validrefs(str0, r0 ' + refs1, ty0, st0) ⊦ r = jvmref, junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs1, st[r -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
st[r -- i '] = refval(r0), junkrefs(str, (r0 ' + refs1) + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, ∀ str0, refs2, ty0, st0. junkrefs(str0, (r0 ' + refs1) + refs2, ty0, st0) → junkrefs(str0, r0 ' + refs1, ty0, st0) ∨ validrefs(str0, r0 ' + refs1, ty0, st0) ⊦ r = jvmref, junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), validrefs(str, r0 ' + 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)])]]