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Proof step 13 from proof newref-newreflist-subset (previous step)

0 < m +1, ∀ r, st, st0. r ∈ newref_list(m, st) ∧ st0 ⊆ st → newref(r, st0) ⊦ r ∈ newref(st) + newref_list(m +1 -1, st[newref(st) -- 0 ', noval]) ∧ st0 ⊆ st → newref(r, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ newref(r, st) ↔ r ≠ jvmref ∧ (∀ rk. rk ∈ st → rk .ref ≠ r)
Proof step 5:
⊦ ¬ newref(newref(st), st0) → ¬ st0 ⊆ st
Proof step 12:
st0 ⊆ st, r ∈ newref_list(m, st[newref(st) -- 0 ', noval]), ∀ r0, st1, st2. r0 ∈ newref_list(m, st1) ∧ st2 ⊆ st1 → r0 ≠ jvmref ∧ (∀ rk. rk ∈ st2 → rk .ref ≠ r0) ⊦ r = newref(st), newref(r, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ (m + 1) -1 = m], [CSIMPSEQ : ⊦ m +1 = m + 1])]]