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Proof step 100 from proof validrefs-junkrefs (conclusion)

⊦ junkrefs(str, refs, ty, st) → (∃ refs0, r, refs1. refs = refs0 + r ' + refs1 ∧ validrefs(str, refs0, ty, st) ∧ r ≠ jvmref ∧ ( ¬ is_valid_ref(str, r, st) ∨ refs0 = [] ∧ ¬ st[r -- _type] .type ≤ ty ∨ refs0 ≠ [] ∧ ( is_obj(refs0 .last, st) ∧ (∃ fs. fs ' ∈ instfields(st[refs0 .last -- _type] .type .class) ∧ is_referencevalue(st[refs0 .last -- fs ']) ∧ r = st[refs0 .last -- fs '] .refval ∧ ¬ st[r -- _type] .type ≤ fs .type) ∨ is_array(refs0 .last, st) ∧ (∃ i. 0 ≤ i ∧ i < st[refs0 .last -- _length] .intval ∧ is_referencevalue(st[refs0 .last -- i ']) ∧ r = st[refs0 .last -- i '] .refval ∧ ¬ st[r -- _type] .type ≤ st[refs0 .last -- _type] .type .type))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
junkrefs(str, refs, ty, st) ⊦ ∃ refs0, r, refs1. refs = refs0 + r ' + refs1 ∧ validrefs(str, refs0, ty, st) ∧ r ≠ jvmref ∧ ( ¬ is_valid_ref(str, r, st) ∨ refs0 = [] ∧ ¬ st[r -- _type] .type ≤ ty ∨ refs0 ≠ [] ∧ ( is_obj(refs0 .last, st) ∧ (∃ fs. fs ' ∈ instfields(st[refs0 .last -- _type] .type .class) ∧ is_referencevalue(st[refs0 .last -- fs ']) ∧ r = st[refs0 .last -- fs '] .refval ∧ ¬ st[st[refs0 .last -- fs '] .refval -- _type] .type ≤ fs .type) ∨ is_array(refs0 .last, st) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[refs0 .last -- _length] .intval ≤ i ∧ is_referencevalue(st[refs0 .last -- i ']) ∧ r = st[refs0 .last -- i '] .refval ∧ ¬ st[st[refs0 .last -- i '] .refval -- _type] .type ≤ st[refs0 .last -- _type] .type .type)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]