Actual signed finite support — Exact Proof Explorer

Prove that a genuine zero tail does not alter an actual finite signed sum.

8 theorem bodies · 25 proof edges · 312 tactic lines · 4 layers

Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable

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

8 theorems
0123
ZS0001 · signed_zero_window_empty

A half-open zero window with coinciding endpoints is genuinely empty.

layer 0 · 13 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable
ZS0002 · signed_zero_window_restrict

Restrict the upper endpoint of an actual zero window without changing any represented values.

layer 0 · 22 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable
ZS0003 · signed_zero_window_raise_lower

Raise the lower endpoint of a zero window, retaining its actual pointwise meaning.

layer 0 · 22 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable
ZS0004 · signed_prefix_sum_zero_tail

Ordinary finite induction proves that a genuinely zero tail changes no actual canonical signed prefix sum.

layer 1 · 103 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable
ZS0005 · signed_prefix_sum_zero_value

A genuinely all-zero represented prefix has canonical signed sum zero; the proof retains actual fold witnesses.

layer 2 · 34 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable
ZS0006 · signed_prefix_sum_zero_exists

Construct the actual sum of a valid all-zero prefix and prove its value, without postulating a sum oracle.

layer 3 · 21 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable
ZS0007 · signed_prefix_sum_last_value

If a prefix is zero, its next actual sum is precisely the actual last entry, including the l=0 boundary.

layer 3 · 44 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable
ZS0008 · signed_prefix_sum_zero_padding_iff

Actually construct either fold from the other across a proved zero tail; both implications retain real finite-sum witnesses.

layer 2 · 53 lines · Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

Exactly 8 displayed theorems have independently verified Alpha checked-use authority; none is admitted to Stable. Body-only enrollment never grants checked theorem use.