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Proof step 98 from proof validrefs-junkrefs (previous step)

∀ str, ty, st. junkrefs(str, acc, ty, st) → (∃ refs0, r, refs1. acc = 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)))), junkrefs(str, r + acc, ty, st) ⊦ ∃ refs0, r0, refs1. r + acc = refs0 + r0 ' + refs1 ∧ validrefs(str, refs0, ty, st) ∧ r0 ≠ jvmref ∧ ( ¬ is_valid_ref(str, r0, st) ∨ refs0 = [] ∧ ¬ st[r0 -- _type] .type ≤ ty ∨ refs0 ≠ [] ∧ ( is_obj(refs0 .last, st) ∧ (∃ fs. fs ' ∈ instfields(st[refs0 .last -- _type] .type .class) ∧ is_referencevalue(st[refs0 .last -- fs ']) ∧ r0 = 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 ']) ∧ r0 = st[refs0 .last -- i '] .refval ∧ ¬ st[st[refs0 .last -- i '] .refval -- _type] .type ≤ st[refs0 .last -- _type] .type .type)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
junkrefs(str, r ' + acc, ty, st), ∀ str0, ty0, st0. junkrefs(str0, acc, ty0, st0) → (∃ refs, r0, refs0. acc = refs + r0 ' + refs0 ∧ validrefs(str0, refs, ty0, st0) ∧ r0 ≠ jvmref ∧ ( ¬ is_valid_ref(str0, r0, st0) ∨ refs = [] ∧ ¬ st0[r0 -- _type] .type ≤ ty0 ∨ refs ≠ [] ∧ ( is_obj(refs .last, st0) ∧ (∃ fs. fs ' ∈ instfields(st0[refs .last -- _type] .type .class) ∧ is_referencevalue(st0[refs .last -- fs ']) ∧ r0 = st0[refs .last -- fs '] .refval ∧ ¬ st0[st0[refs .last -- fs '] .refval -- _type] .type ≤ fs .type) ∨ is_array(refs .last, st0) ∧ (∃ i. 0 ≤ i ∧ i < st0[refs .last -- _length] .intval ∧ is_referencevalue(st0[refs .last -- i ']) ∧ r0 = st0[refs .last -- i '] .refval ∧ ¬ st0[st0[refs .last -- i '] .refval -- _type] .type ≤ st0[refs .last -- _type] .type .type)))) ⊦ ∃ refs, r0, refs0. r ' + acc = refs + r0 ' + refs0 ∧ validrefs(str, refs, ty, st) ∧ r0 ≠ jvmref ∧ ( ¬ is_valid_ref(str, r0, st) ∨ refs = [] ∧ ¬ st[r0 -- _type] .type ≤ ty ∨ refs ≠ [] ∧ ( is_obj(refs .last, st) ∧ (∃ fs. fs ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_referencevalue(st[refs .last -- fs ']) ∧ r0 = st[refs .last -- fs '] .refval ∧ ¬ st[st[refs .last -- fs '] .refval -- _type] .type ≤ fs .type) ∨ is_array(refs .last, st) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[refs .last -- _length] .intval ≤ i ∧ is_referencevalue(st[refs .last -- i ']) ∧ r0 = st[refs .last -- i '] .refval ∧ ¬ st[st[refs .last -- i '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]