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Proof step 8 from proof ascsubseq-in-size (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var:ix0

Additional information

[Concretesimprules((Csimpnamedseq(ascsubseq-single,,, ⊦ ascsubseq(n ', x) ↔ n < # x) Csimpgen(ilist freely generated by [], +;) Csimpnamedseq(list,indexseq,app, ⊦ ix + [] = ix) Csimpnamedseq(list,indexseq,a, ⊦ (ix + ix0) + ix1 = ix + ix0 + ix1) Csimpnamedseq(list,indexseq,in-empty, ⊦ ¬ n ∈ []) Csimpnamedforward(nat,,fle, ⊦ m < n ∧ n ≤ n0 → m < n0) Csimpnamedforward(nat-basic1,,lf-02, ⊦ m < n ∧ m = n0 → n0 < n) Csimpnamedforward(nat-basic1,,f, ⊦ m < n → n ≠ 0) Csimpnamedseq(list-data,,l, ⊦ # x = 0 ↔ x = []) Csimpnamedseq(oelem,indexseq,irreflexivity, ⊦ ¬ n < n)))]