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Proof step 16 from proof validref-array-rec (previous step)

is_array(str, r, st), is_array(str, r, st), st[r -- _type] .type ≤ ty ⊦ r = jvmref, ¬ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st))) ↔ (∀ i. ¬ 0 ≤ i ∨ ¬ i < st[r -- _length] .intval ∨ ¬ is_referencevalue(st[r -- i ']) ∨ st[r -- i '] .refval = jvmref ∨ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ validref(str, st[r -- i '] .refval, st[r -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
is_array(str, r, st), st[r -- _type] .type ≤ ty ⊦ r = jvmref, (∀ i. i < 0 ∨ st[r -- _length] .intval ≤ i ∨ ¬ is_referencevalue(st[r -- i ']) ∨ st[r -- i '] .refval = jvmref ∨ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ ¬ junkref(str, st[r -- i '] .refval, st)) ↔ (∀ i. ¬ 0 ≤ i ∨ ¬ i < st[r -- _length] .intval ∨ ¬ is_referencevalue(st[r -- i ']) ∨ st[r -- i '] .refval = jvmref ∨ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ validref(str, st[r -- i '] .refval, st[r -- _type] .type .type, st))

Rule argument

[emptyarg]

Additional information

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