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refactor(MultiTape): remove the deterministic space measures - #1122
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Renames `MultiTapeTM.spaceUsed` to `space`, matching `RunPath.space` and `ComputationPath.space`: `tm.space cfg t` is the space of the path of the first `t` steps from `cfg`. The lemmas named after it follow. Depends on leanprover#1117: its commits are included temporarily and will leave this diff when that PR merges. The stack continues in leanprover#1122. Composed with Claude Code. Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
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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>
Space is counted only on run and computation paths. The visitation and displacement lemmas hold for the run paths of nondeterministic machines, and the configuration bounds take `RunsInSpace` and count the storages and cores at the ends of computation paths: the computation paths of a deterministic machine are prefixes of one another, so the one visiting the most cells contains the windows of every other. The deterministic `visitedByTapeHead`, `spaceUsedByTape` and `space` go, with their lemmas and the unused `core_step_eq_of_core_eq`. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Removes
MultiTapeTM.visitedByTapeHead,spaceUsedByTapeandspace, so space is counted only on run and computation paths. The visitation and displacement lemmas move to run paths and hold for nondeterministic machines.Counts the storages and cores in
ConfigBoundat the ends of computation paths, bounded byRunsInSpace, with unchanged numerical bounds. The computation paths of a deterministic machine are prefixes of one another (RunPath.eq_take), so the one visiting the most cells contains the windows of every other.Depends on #1145: its commit is included temporarily and will leave this diff when it merges.
Composed with Claude Code.