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Proof step 9 from proof ascsubseq-in-size (previous step)

∀ n, x. ¬(n ∈ ix0 ∧ ascsubseq(ix0, x) ∧ # x ≤ n), n ∈ m + ix0, ascsubseq(m + ix0, x), # x ≤ n ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# x ≤ n, ascsubseq(m ' + ix0, x), ∀ n0, x0. ¬ n0 ∈ ix0 ∨ ¬ ascsubseq(ix0, x0) ∨ ¬ # x0 ≤ n0 ⊦ n ≠ m ∧ ¬ n ∈ ix0

Rule argument

Additional information

[Concretesimprules((Csimpnamedseq(list,indexseq,a, ⊦ (ix + ix0) + ix1 = ix + ix0 + ix1) Csimpnamedseq(list,indexseq,in-17, ⊦ n ∈ n0 ' ↔ n = n0) Csimpnamedseq(list,indexseq,in-append, ⊦ n ∈ ix + ix0 ↔ ¬ ¬(n ∈ ix ∨ n ∈ ix0)) Csimpnamedseq(list,indexseq,c, ⊦ n + ix = n ' + ix)))]