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Proof step 57 from proof validrefs-put-notin-03 (previous step)

r -- i ' ≠ r -- sk, st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st[r -- sk, val]), is_valid_ref(r, st), is_array(str, r, st), validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st) ⊦ r = jvmref, r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, r ∈ refs1, dups(refs1), r0 ∈ refs1, is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs1, st[r -- _type] .type .type, st[r -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), is_array(str, r, st), is_valid_ref(r, st), is_array(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ i ' = sk, sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r = jvmref, r0 ∈ refs1, dups(refs1), r ∈ refs1, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st[r -- sk, 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 : refkey, , inj-01, ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]