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Proof step 44 from proof validrefs-maxlen (previous step)

∀ str, ty, st. validrefs(str, acc, ty, st) ∧ acc ≠ [] ∧ ¬ dups(acc) → # acc ≤ # st .refs + 1 ⊦ validrefs(str, r + acc, ty, st) ∧ r + acc ≠ [] ∧ ¬ dups(r + acc) → # (r + acc) ≤ # st .refs + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# st .refs < # acc, validrefs(str, r ' + acc, ty, st), ∀ str0, ty0, st0. validrefs(str0, acc, ty0, st0) → # acc ≤ # st0 .refs + 1 ⊦ acc = [], r ∈ acc, dups(acc)

Rule argument

[emptyarg]

Additional information

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