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Proof step 4 from proof precedesex-prepend (previous step)

precedes∃(ix ' + ixs, x) ⊦ precedes∃(ixs, x)

User applied rule constructor cut

And closed the goal!

Rule argument

var:ixs

Additional information

[Concretesimprules((Csimpnamedseq(precedesex-rec0,,, ⊦ precedes∃(ix ', x)) Csimpnamedseq(precedesex-base,,, ⊦ precedes∃([], x)) Csimpnamedseq(precedesex-rec1,,, ⊦ precedes∃ (ix0 ' + ix1 ' + ixs, x) ↔ precedes∃(ix1 ' + ixs, x) ∧ (∀ n1. n1 ∈ ix1 → (∃ n0. n0 ∈ ix0 ∧ precedes (n0, n1, x)))) Csimpgen(illist freely generated by [], +;) Csimpnamedseq(list,indexseq-stackseq,c, ⊦ ix + ixs = ix ' + ixs) Csimpnamedseq(list,indexseq-stackseq,a, ⊦ (ixs + ixs0) + ixs1 = ixs + ixs0 + ixs1) Csimpnamedseq(list,indexseq-stackseq,app, ⊦ ixs + [] = ixs)))]