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Proof step 83 from proof validref-refs-last-valid-subset (previous step)

is_array(str, r0, st0) ∧ st0[r0 -- _type] .type ≤ ty, st0[r0 -- _type] .type ≤ ty, validref(str, r, st[r -- _type] .type, st), st ⊆ st0, acc + r1 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st0[r0 -- _length] .intval ∧ is_referencevalue(st0[r0 -- i ']) ∧ (acc + r1 ') .first = st0[r0 -- i '] .refval ∧ validrefs(str, acc + r1 ', st0[r0 -- _type] .type .type, st0)), is_array(str, r0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 82:
(acc + r1 ') .first = st0[r0 -- i '] .refval, st0[r0 -- _type] .type ≤ ty, validref(str, r, st[r -- _type] .type, st), st ⊆ st0, is_array(str, r0, st0), i < st0[r0 -- _length] .intval, is_referencevalue(st0[r0 -- i ']), validrefs(str, acc + r1 ', st0[r0 -- _type] .type .type, st0), 0 ≤ i, 0 < st0[r0 -- _length] .intval, ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]