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Proof step 29 from proof validrefs-delete-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
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, ∀ str, ty, st, r. validrefs(str, acc, ty, st) → r ∈ acc ∨ validrefs(str, acc, ty, st -- r) ⊦ r = r0, r0 = jvmref, acc = [], r ∈ acc, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ acc .first = st[r0 -- i0 '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st -- r)

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 : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array(str, r0, st -- r) ↔ is_array(str, r0, st))])]]