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Proof step 29 from proof junkrefs-delete-02 (previous step)

is_array(str, r0, st -- r) ∧ (st -- r)[r0 -- _type] .type ≤ ty, st[r0 -- i '] = refval(r2), junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, is_array(str, r0, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st0, r1. junkrefs(str0, r2 ' + refs, ty0, st0) → junkrefs(str0, r2 ' + refs, ty0, st0 -- r1) ⊦ r0 = jvmref, r = r0, r2 ' + refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st -- r)[r0 -- _length] .intval ∧ is_referencevalue((st -- r)[r0 -- i ']) ∧ (r2 ' + refs) .first = (st -- r)[r0 -- i '] .refval ∧ junkrefs(str, r2 ' + refs, (st -- r)[r0 -- _type] .type .type, st -- r))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
st[r0 -- i '] = refval(r2), junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, 0 < st[r0 -- _length] .intval, 0 ≤ i, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st0, r1. junkrefs(str0, r2 ' + refs, ty0, st0) → junkrefs(str0, r2 ' + refs, ty0, st0 -- r1) ⊦ r0 = jvmref, r = r0, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r2 = st[r0 -- i0 '] .refval ∧ junkrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st -- r)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array(str, r0, st -- r) ↔ is_array(str, r0, st))])]]