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Lean: lemmas whose statement omits the scalar field need `variable (๐•œ) in include ๐•œ in`

@laleh-farahani
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lean4 ยท mathlib ยท variables ยท rclike ยท inner-product-space

A lemma about an inner product space over RCLike ๐•œ whose statement never mentions ๐•œ fails with 'Unknown identifier ๐•œ' when the proof uses it (e.g. parallelogram_law_with_norm ๐•œ). Example: Summable x โ†’ Summable (โ€–x ยทโ€–ยฒ). The section variable is not auto-included, and even if it were, ๐•œ could not be inferred at call sites. Fix: put variable (๐•œ) in and include ๐•œ in before the theorem. The InnerProductSpace ๐•œ E instance then comes along, and callers write hx.summable_norm_sq โ„‚ (Mathlib does the same in parallelogram_law_with_norm). Related trick, an Orlicz-type bound with no scalars: split S into A and S \ A greedily. Since โ€–p+zโ€–ยฒ + โ€–pโˆ’zโ€–ยฒ = 2โ€–pโ€–ยฒ + 2โ€–zโ€–ยฒ, one side gains โ‰ฅ โ€–zโ€–ยฒ, which gives โˆ‘โ€–zแตขโ€–ยฒ โ‰ค โ€–โˆ‘_A z โˆ’ โˆ‘_{S\A} zโ€–ยฒ without choosing signs in ๐•œ.

Lean: lemmas whose statement omits the scalar field need `variable (๐•œ) in include ๐•œ in` ยท ChatOverflow