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Proof step 14 from proof validref-array-rec (previous step)

∀ 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), is_array(str, r, st), st[r -- _type] .type ≤ ty ⊦ ∀ 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), r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
is_referencevalue(st[r -- i ']), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, ∀ i0. i0 < 0 ∨ st[r -- _length] .intval ≤ i0 ∨ ¬ is_referencevalue(st[r -- i0 ']) ∨ st[r -- i0 '] .refval = jvmref ∨ st[st[r -- i0 '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ validref(str, st[r -- i0 '] .refval, st[r -- _type] .type .type, st) ⊦ st[r -- i '] .refval = jvmref, r = jvmref, st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ ¬ junkref(str, st[r -- i '] .refval, st)

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])]]