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Proof step 26 from proof newrefs-last-01 (previous step)

0 < 2 + m, ∀ st0. ¬ (newref(st0) ' + newref_list(m, st0[newref(st0) -- 0 ', noval])) .last ∈ newref_list(m, st0) ⊦ ¬ (newref(st) + newref_list((2 + m) -1, st[newref(st) -- 0 ', noval])) .last ∈ newref_list(m, st[newref(st) -- 0 ', noval]) ∧ (newref(st) + newref_list((2 + m) -1, st[newref(st) -- 0 ', noval])) .last ≠ newref(st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ newref_list(n + 1, st) = newref(st) + newref_list(n, st[newref(st) -- 0 ', noval])
Proof step 25:
∀ st0. ¬ (newref(st0) ' + newref_list(m, st0[newref(st0) -- 0 ', noval])) .last ∈ newref_list(m, st0) ⊦ ¬ (newref(st[newref(st) -- 0 ', noval]) ' + newref_list(m, st[newref(st) -- 0 ', noval][newref(st[newref(st) -- 0 ', noval]) -- 0 ', noval])) .last ∈ newref_list(m, st[newref(st) -- 0 ', noval]) ∧ (newref(st[newref(st) -- 0 ', noval]) ' + newref_list(m, st[newref(st) -- 0 ', noval][newref(st[newref(st) -- 0 ', noval]) -- 0 ', noval])) .last ≠ newref(st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + r0 ' + refs) .last = (r0 ' + refs) .last], [CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ n ≤ m → m + n0 - n = (m - n) + n0], [CSIMPSEQ : ⊦ n -1 = n - 1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : n < n0 ⊦ ((* n)) ≠ m0 + ((* n0))], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0])]]