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Proof step 23 from proof junkref-primarray-level-01 (previous step)

is_array(str1, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str1, r, st), ∀ str1, st0, r1, str, refs. # refs < # (r0 + refs1) → ( junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → has_classtype(st0[r1 -- _type] .type) ∨ junkrefs(str1, r1 ' + refs, st0[r1 -- _type] .type, st0)) ⊦ r = jvmref, r0 ' + refs1 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r0 ' + refs1) .first = st[r -- i '] .refval ∧ junkrefs(str1, r0 ' + refs1, st[r -- _type] .type .type, st)), has_classtype(st[r -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str1, r, st), ∀ str1, st0, r1, str, refs. # refs < # (r0 + refs1) → ( junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → has_classtype(st0[r1 -- _type] .type) ∨ junkrefs(str1, r1 ' + refs, st0[r1 -- _type] .type, st0)) ⊦ r = jvmref, has_classtype(st[r -- _type] .type), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ junkrefs(str1, st[r -- i0 '] .refval ' + refs1, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ ¬ has_classtype(ty) → (ty0 ≤ ty ↔ ty0 = ty)])]]