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Proof step 22 from proof validrefs-not-in (previous step)

is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ r, str, ty, st. r ∈ acc ∧ validrefs(str, acc, ty, st) → r = jvmref ∨ is_valid_ref(r, st) ∧ type∃(str, st[r -- _type] .type), acc = [] ∨ 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ acc .first = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st) ⊦ acc = [], r0 = jvmref, r = jvmref, r ≠ r0 ∧ ¬ r ∈ acc, is_valid_ref(r, st) ∧ type∃(str, st[r -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
acc .first = st[r0 -- i '] .refval, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, acc, st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ r, str, ty, st. r ∈ acc ∧ validrefs(str, acc, ty, st) → r = jvmref ∨ is_valid_ref(r, st) ∧ type∃(str, st[r -- _type] .type) ⊦ acc = [], r0 = jvmref, r = jvmref, r ≠ r0 ∧ ¬ r ∈ acc, is_valid_ref(r, st) ∧ type∃(str, st[r -- _type] .type)

Rule argument

[emptyarg]

Additional information

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