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Proof step 48 from proof validrefs-put-array-badindex (previous step)

st[r0 -- i0 '] = refval(r2), i < st[r0 -- _length] .intval, validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st), is_array(str, r0, st), i < 0, is_array(str, r0, st[r -- i ', val]), st[r0 -- _type] .type ≤ ty, i0 < st[r0 -- _length] .intval, 0 ≤ i0, 0 < st[r0 -- _length] .intval, ∀ i, str0, ty0, st0, r1, val0. ¬ 0 ≤ i → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i ', val][r0 -- i0 ']) ∧ r2 = (st[r -- i ', val][r0 -- i0 ']) .refval ∧ validrefs(str, (st[r -- i ', val][r0 -- i0 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
st[r0 -- i0 '] = refval(r2), i < st[r0 -- _length] .intval, validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st), is_array(str, r0, st), i < 0, is_array(str, r0, st[r -- i ', val]), st[r0 -- _type] .type ≤ ty, i0 < st[r0 -- _length] .intval, 0 ≤ i0, 0 < st[r0 -- _length] .intval, ∀ i, str0, ty0, st0, r1, val0. ¬ 0 ≤ i → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, is_referencevalue(st[r -- i ', val][r0 -- i0 ']) ∧ r2 = (st[r -- i ', val][r0 -- i0 ']) .refval ∧ validrefs(str, (st[r -- i ', val][r0 -- i0 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels-03, ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]