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Proof step 102 from proof unchanged-junkrefs-level (previous step)

¬ ( ¬ ( st[r -- _type] = st1[r -- _type] ∧ (is_classtype(st[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) → st[r -- fs '] = st1[r -- fs '])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] = st1[r -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval → st[r -- i '] = st1[r -- i ']))) ∧ r ≠ jvmref), 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, ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r1 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 101:
st[r -- _length] = st1[r -- _length], st[r -- i '] = refval(r1), st1[r -- _type] = st[r -- _type], 0 < st1[r -- _length] .intval, is_array(str0, r, st), unchangedNorec(r, st, st1), is_array(str, r, st), 0 ≤ i, is_array(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, i < st1[r -- _length] .intval, junkrefs(str, r1 ' + refs, st[r -- _type] .type .type, st), is_arraytype(st[r -- _type] .type), unchanged(str0, r, st, st1), level⊆(str, str0), ∀ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st1[r -- i0 '], ∀ 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, is_referencevalue(st1[r -- i ']) ∧ r1 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels-03, ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPNAMEDFORWARD : int-abs, , forward-lels, ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPNAMEDSEQ : javatype, , diff-01, ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPNAMEDSEQ : addfuns, , is_valid_ref-array-01, ⊦ is_arraytype (st[r -- _type] .type) ∧ r ≠ jvmref → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPNAMEDSEQ : addfuns, , is_obj-classtype, ⊦ ¬ is_classtype (st[r -- _type] .type) → ¬ is_obj(str, r, st)], [CSIMPNAMEDSEQ : addfuns, , is_valid_ref-no-arraytype, ⊦ ¬ is_arraytype (st[r -- _type] .type) → ( is_valid_ref(str, r, st) ↔ is_obj(str, r, st))], [CSIMPNAMEDSEQ : okfuns, , is_array-classtype, ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]