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Proof step 28 from proof cyclic-put-nopathex (previous step)

¬ ¬ r0 ∈ (r ' + refs1) + r1 ', validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st) ⊦ validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]), sk = _type, path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, r1 ≠ r ∧ ¬ r1 ∈ refs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 24:
⊦ ¬ is_valid_ref(str, r, st) → (validrefs(str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])
Proof step 25:
⊦ ¬ path∃(str, r, r0, st) → ¬ validrefs(str, r ' + refs + r0 ', ty, st)
Proof step 27:
validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st), r0 ∈ refs1 ⊦ sk = _type, r0 = r1, r0 = r, validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]), path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, r1 ≠ r ∧ ¬ r1 ∈ refs1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)])]]