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Proof step 34 from proof validrefs-delcycle (previous step)

is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, refs1 .last = jvmref, acc + r ' = r1 ' + refs, st[r0 -- i '] = refval(r1), is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, validrefs(str, acc + r ' + refs0 + r ' + refs1, st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, refs1 = [], acc + r ' + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ (acc + r ' + refs1) .first = st[r0 -- i '] .refval ∧ validrefs(str, acc + r ' + refs1, st[r0 -- _type] .type .type, st)), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
st[r0 -- i '] = refval(r1), acc + r ' = r1 ' + refs, refs1 .last = jvmref, 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, acc + r ' + refs0 + r ' + refs1, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ refs1 = [], r0 = jvmref, ¬ r1 ∈ acc ∧ r1 ≠ r, r ≠ r1 ∧ ¬ r ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r1 = st[r0 -- i0 '] .refval ∧ validrefs(str, acc + r ' + refs1, st[r0 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + r ' + refs0) .first = (refs + r ') .first], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + r ' + refs0 ≠ []])]]