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Proof step 119 from proof validrefs-put-notin-03 (previous step)

list2set(refs1) ∩ list2set(refs0) = ∅, is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), refs0 + r ' = r4 ' + refs2, st[r1 -- i '] = refval(r4), validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st), is_valid_ref(r1, st), is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, i < st[r1 -- _length] .intval, 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ str0, r2, st0, sk0, val0, refs, r3, ty0. (is_valid_ref(str0, r2, st0) ↔ is_valid_ref(str0, r2, st0[r2 -- sk0, val0])) ∧ list2set(refs0) ∩ list2set(refs) = ∅ → val0 .refval = r3 ∨ r3 = st0[r2 -- sk0] .refval ∨ sk0 = _type ∨ sk0 = _length ∨ (validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0)) ∨ r2 = r3 ∨ r3 ∈ refs0 ∨ r2 ∈ refs ∨ r2 ∈ refs0 ∨ dups(refs) ∨ r3 ∈ refs ⊦ sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r1 = jvmref, r = r1, r0 = r1, r ∈ refs0, r ∈ refs1, r0 ∈ refs0, r1 ∈ refs0, dups(refs0), r1 ∈ refs1, r0 ∈ refs1, dups(refs1), ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ r4 = st[r1 -- i '] .refval ∧ validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st[r -- sk, val]), r ≠ r4 ∧ ¬ r ∈ refs2, ¬ r4 ∈ refs0 ∧ r4 ≠ r

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 118:
st[r1 -- i '] = refval(r4), refs0 + r ' = r4 ' + refs2, is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), list2set(refs1) ∩ list2set(refs0) = ∅, 0 < st[r1 -- _length] .intval, 0 ≤ i, i < st[r1 -- _length] .intval, st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), is_valid_ref(r1, st), validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st), ∀ str0, r2, st0, sk0, val0, refs, r3, ty0. (is_valid_ref(str0, r2, st0) ↔ is_valid_ref(str0, r2, st0[r2 -- sk0, val0])) ∧ list2set(refs0) ∩ list2set(refs) = ∅ → val0 .refval = r3 ∨ r3 = st0[r2 -- sk0] .refval ∨ sk0 = _type ∨ sk0 = _length ∨ (validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0)) ∨ r2 = r3 ∨ r3 ∈ refs0 ∨ r2 ∈ refs ∨ r2 ∈ refs0 ∨ dups(refs) ∨ r3 ∈ refs ⊦ r0 = r1, r = r1, r1 = jvmref, r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, dups(refs1), r0 ∈ refs1, r1 ∈ refs1, dups(refs0), r1 ∈ refs0, r0 ∈ refs0, r ∈ refs1, r ∈ refs0, validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st[r -- sk, val]), ¬ r4 ∈ refs0 ∧ r4 ≠ r, r ≠ r4 ∧ ¬ r ∈ refs2

Rule argument

[emptyarg]

Additional information

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