Actual pointwise operations · signed values · distributivity · Constructive arithmetic

Signed weighted sums and linearity

ArithAdd(F,G,H,l) ∧ SignedWeightedSum(W,F,l,a) ∧ SignedWeightedSum(W,G,l,b) ∧ SignedWeightedSum(W,H,l,c) ⇒ SignedAdd(a,b,c)

Construct real pointwise sum, product and scalar tables and prove algebraic laws for their actual finite signed sums, including empty windows.

Open the definition-aware map Read the final theorem See campaign milestone G007

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.

Exact certificate

Fully expanded arithmetic

Inspect all 2117 native tactic lines and 121 actual proof prerequisites with every definition fully expanded.

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Focused route

Final dependency cone

Start at theorem WS0027 and follow only the lemmas and conservative definitions supporting signed_weighted_sum_add_linearity.

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Zoom between mathematical scales: complete research atlas → research domain → proof family → G007 milestone → theorem and definition dependencies.
Major independently established statements: WS0021 signed_weighted_sum_exists_unique · WS0028 signed_weighted_sum_scalar_linearity · WS0027 signed_weighted_sum_add_linearity.
Independently verified Alpha v34 checked-use theorem family: 40 dependency-curried kernel-checked theorem bodies · 121 proof prerequisites · 18 linked definitions · 34 definition-dependency arrows · 2117 exact tactic lines · first admitted v31 · not Stable. The unchanged intuitionistic kernel and separately compiled Lean verifier independently accept all 227 bundle nodes; SHA-256 e88ddec495a71d673e670299ea3943a5a996eecb1296fb746e107c8e0b81c967.
Exact mathematical boundary: Operation tables contain actual beta-coded entries and compare represented signed values, not encodings. The strict sum window is i<l and the separately certified endpoint i=l is unused. Rectangular Fubini and full finite signed Möbius inversion are separate, now-admitted families.