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Proof step 106 from proof unchanged-junkrefs-level (previous step)

st[r -- i '] = refval(r1), st1[r -- _type] = st[r -- _type], unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_array(str, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, r1 ' + refs, st[r -- _type] .type .type, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ str1, st0, st2, str2, ty0. unchanged(str1, r1, st0, st2) ∧ junkrefs(str2, r1 ' + refs, ty0, st0) ∧ level⊆(str2, str1) → junkrefs(str2, r1 ' + refs, ty0, st2) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st1[r -- i0 ']) ∧ r1 = st1[r -- i0 '] .refval ∧ junkrefs(str, r1 ' + refs, st[r -- _type] .type .type, st1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 105:
st1[r -- _type] = st[r -- _type], st[r -- i '] = refval(r1), junkrefs(str, r1 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_valid_ref(str0, r, st1), is_array(str, r, st1), 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), unchangedNorec(r, st, st1), is_valid_ref(str0, r, st), level⊆(str, str0), unchanged(str0, r, st, st1), ∀ str1, st0, st2, str2, ty0. unchanged(str1, r1, st0, st2) ∧ junkrefs(str2, r1 ' + refs, ty0, st0) ∧ level⊆(str2, str1) → junkrefs(str2, r1 ' + refs, ty0, st2), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st1[r -- i0 ']) ∧ r1 = st1[r -- i0 '] .refval ∧ junkrefs(str, st1[r -- i0 '] .refval ' + refs, st[r -- _type] .type .type, st1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]