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Proof step 12 from proof cyclic-def-simple (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, is_array(str, r, st), dups(refs1) ∨ r ∈ refs1, refs1 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs1 .first = st[r -- i '] .refval ∧ validrefs(str, refs1, st[r -- _type] .type .type, st) ⊦ r = jvmref, refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs1 .first = st[r -- i '] .refval ∧ validrefs(str, refs1, st[r -- _type] .type .type, st)), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
refs1 .first = st[r -- i '] .refval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs1, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, dups(refs1) ∨ r ∈ refs1 ⊦ r = jvmref, refs1 = [], ¬ r ∈ refs1 ∧ ¬ dups(refs1), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ refs1 .first = st[r -- i0 '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty ≤ ty])]]