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Proof step 46 from proof validrefs-put-array-badindex (previous step)

r0 -- i0 ' ≠ r -- i ', 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[r0 -- i0 ']) ∧ r2 = st[r0 -- i0 '] .refval ∧ validrefs(str, st[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 45:
st[r0 -- i0 '] = refval(r2), 0 < st[r0 -- _length] .intval, 0 ≤ i0, i0 < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- i ', val]), i < 0, is_array(str, r0, st), validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st), i < 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)) ⊦ i0 = i, r0 = jvmref, validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : int-abs, , lels-03, ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPNAMEDSEQ : storekey, , inj-04, ⊦ i ' = i0 ' ↔ i = i0], [CSIMPNAMEDSEQ : refkey, , inj-01, ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]