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Proof step 33 from proof validrefs-put-notin (previous step)

st[r0 -- i '] = refval(r1), 0 < st[r0 -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st[r -- sk, val]), i < st[r0 -- _length] .intval, ∀ str0, ty0, st0, r2, sk0, val0. (validrefs(str0, r1 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, r1 ' + refs, ty0, st0)) ∨ r2 = r1 ∨ r2 ∈ refs ⊦ r = r1, r = r0, r0 = jvmref, r ∈ refs, ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
st[r0 -- i '] = refval(r1), i < st[r0 -- _length] .intval, validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st[r -- sk, val]), is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str0, ty0, st0, r2, sk0, val0. (validrefs(str0, r1 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, r1 ' + refs, ty0, st0)) ∨ r2 = r1 ∨ r2 ∈ refs ⊦ r0 = jvmref, r = r0, r = r1, r ∈ refs, validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]