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refactor(MultiTape): rename spaceUsed to space - #1133
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Match the space vocabulary of `Space.lean`, where the cells visited by all tapes of a path are its `space`: `tm.space cfg t` is the space of the path of the first `t` steps from `cfg`. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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…ugh run paths (leanprover#1117) Expresses the tape simulations, tape specifications and sequential composition through run paths. `stepHom` reads a semiconjugation of `step` as a homomorphism of the step relations, which maps run paths, and each of `extendTapes`, `outputToTape` and `inputFromTape` bounds the space of the mapped path through `RunPath.space_map_le`, replacing the per-file iteration and space proofs. `spaceUsed` becomes an abbreviation for the space of the path of the first `t` steps, so `TransformsTapes` keeps its statement. Sequential composition derives its space bound from the existing state-free invariant. The deterministic space lemmas used only by these proofs and the unused `Cfg.withOutput` are removed. The stack continues in leanprover#1133. Composed with Claude Code. --------- Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
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Renames
MultiTapeTM.spaceUsedtospace, matchingRunPath.spaceandComputationPath.space:tm.space cfg tis the space of the path of the firsttsteps fromcfg. The lemmas named after it follow.Depends on #1117: its commits are included temporarily and will leave this diff when that PR merges. The stack continues in #1122.
Composed with Claude Code.