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Why do we need this again? |
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It's often a nicer constructor than the regular one. If you read ONAG you'll notice Conway defines his series as sums |
plp127
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Apr 1, 2026
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| simp_rw [mk.injEq, heq_eq_eq, true_and] | ||
| constructor <;> ext | ||
| · exact he .. | ||
| · exact hc .. |
Contributor
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Does this work?
Suggested change
| simp_rw [mk.injEq, heq_eq_eq, true_and] | |
| constructor <;> ext | |
| · exact he .. | |
| · exact hc .. | |
| cases funext fun t : Iio _ => he t.1 t.2 | |
| cases funext fun t : Iio _ => hc t.1 t.2 | |
| rfl |
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Ah lemme try again
Suggested change
| simp_rw [mk.injEq, heq_eq_eq, true_and] | |
| constructor <;> ext | |
| · exact he .. | |
| · exact hc .. | |
| cases funext fun t : Iio _ => he t.1 t.2 t.2 | |
| cases funext fun t : Iio _ => hc t.1 t.2 t.2 | |
| rfl |
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Still no. I get a "Dependent elimination failed" error.
plp127
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Apr 17, 2026
| coeffIdx s i = s.coeff ⟨i, h⟩ := by | ||
| rw [coeffIdx_of_lt (by simpa), exp_coe, coeff_coe] | ||
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| theorem coeffIdx_coe_of_le {s : TermSeq} {i} (h : s.length ≤ i) : coeffIdx s i = 0 := |
| term s i = s.coeff ⟨i, h⟩ * ω^ s.exp ⟨i, h⟩ := by | ||
| rw [term_of_lt (by simpa), coeffIdx_coe_of_lt, exp_coe] | ||
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| theorem term_coe_of_le {s : TermSeq} {i} (h : s.length ≤ i) : term s i = 0 := |
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Same here, use _of_ge to match the _of_lt theorem.
| ofSurrealHahnSeries x = ofSurrealHahnSeries y ↔ x = y := | ||
| surrealHahnSeriesEquiv.symm.apply_eq_iff_eq | ||
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| end TermSeq |
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| end TermSeq | |
| end TermSeq | |
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We define an auxiliary type
TermSeqfor an ordinal-indexed sequence of termsr * ω^ iwith non-zero coefficients and decreasing exponents. These provide an alternate, often more convenient representation for surreal Hahn series. We provide basic API, and build the equiv between both types.