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Proof step 41 from proof validrefs-put-array-badindex (previous step)

(st[r -- i ', val][r0 -- i0 ']) = refval(r2), 0 < st[r0 -- _length] .intval, 0 ≤ i0, 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[r -- i ', val]), is_referencevalue(st[r -- i ', val][r0 -- i0 ']), i0 < st[r0 -- _length] .intval, i < st[r0 -- _length] .intval, ∀ i1, str0, ty0, st0, r1, val0. ¬ 0 ≤ i1 → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i1 ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r0 -- i1 ']) ∧ r2 = st[r0 -- i1 '] .refval ∧ validrefs(str, st[r0 -- i1 '] .refval ' + refs, st[r0 -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
(st[r -- i ', val][r0 -- i0 ']) = refval(r2), i < st[r0 -- _length] .intval, i0 < st[r0 -- _length] .intval, validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val]), is_array(str, r0, st), i < 0, is_array(str, r0, st[r -- i ', val]), st[r0 -- _type] .type ≤ ty, 0 ≤ i0, 0 < st[r0 -- _length] .intval, ∀ i1, str0, ty0, st0, r1, val0. ¬ 0 ≤ i1 → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i1 ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r0 -- i1 ']) ∧ r2 = st[r0 -- i1 '] .refval ∧ validrefs(str, st[r0 -- i1 '] .refval ' + refs, st[r0 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))])]]