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refactor(MultiTape): keep the run path space API in Space.lean - #1145
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The windows, the bounds of a path's space by sets containing its head positions, and the space of a mapped path move from TapeLemmas.lean to Space.lean, next to the space measures; `prependOutputHom` moves to Nondeterministic.lean. Prepending output keeps every head in place, so `transformsTapes_iff_nil_output` reuses the space bound as it is, and the then unused `space_map_eq` goes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Moves the space API of run paths from
TapeLemmas.leantoSpace.lean, next to the space measures: the windows[-s, s], the bounds of a path's space by sets containing its head positions, and the space of a mapped path.prependOutputHommoves toNondeterministic.lean.Restates
space_map_leso that the map carries each head to its tape at every configuration, and removes the unusedspace_le_of_subset,visitedByTapeHead_mapandspace_map_eq. Prepending output keeps every head in place, sotransformsTapes_iff_nil_outputreuses the space bound as it is.Composed with Claude Code.