fix: replace duplicate Level 4 with null_space_is_subspace (closes #18)#19
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fix: replace duplicate Level 4 with null_space_is_subspace (closes #18)#19
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LinearMapsWorld Levels 2 and 4 both proved T 0 = 0 (issue #18). Level 5's intro promised a "null space is a subspace" result that didn't exist. This swaps Level 4's exercise to null_space_is_subspace and keeps linear_map_preserves_zero (used in Levels 5, 8, 9, 10) as a term-form helper := zero_in_null_space K V W T hT, since membership in null_space_v T is definitionally T 0 = 0. Removes the now-duplicate NewTheorem announcement of linear_map_preserves_zero from Level 5. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Merge the two repetitive sentences into one and use the term "null space" instead of "the set of vectors that T sends to zero". Replace the vague "complete picture of how linear maps interact with subspace structure" trailer with a concrete forward-pointer to Level 5. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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LinearMapsWorld Levels 2 and 4 both proved T 0 = 0 (issue #18). This swaps Level 4's exercise to null_space_is_subspace and keeps linear_map_preserves_zero (used in Levels 5, 8, 9, 10) as a term-form helper := zero_in_null_space K V W T hT, since membership in null_space_v T is definitionally T 0 = 0. Removes the now-duplicate NewTheorem announcement of linear_map_preserves_zero from Level 5.