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Proof step 53 from proof validrefs-put-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 52:
acc + r0 ' = r1 ' + refs, st[r -- i '] = refval(r1), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r1 ' + refs, st[r -- _type] .type .type, st[r0 -- sk, val]), 0 ≤ i, 0 < st[r -- _length] .intval, st[r1 -- _type] .type ≤ st[r -- _type] .type .type ⊦ sk = _type, r0 = r, r = jvmref, r1 = jvmref, r0 ∈ acc, validrefs(str, r1 ' + refs, st[r -- _type] .type .type, st), junkref(str, r1, st), ¬ junkref(str, acc .first, st) ∧ acc ≠ [], r0 ≠ r1 ∧ ¬ r0 ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]