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EchidnaABI.TacticRecord: prove deferred round-trip lemmas (natToFinToNat + clampRoundtripInRange) #152

@hyperpolymath

Description

@hyperpolymath

Context

src/abi/EchidnaABI/TacticRecord.idr (introduced in commit 4118893 on branch feat/idris2-abi-tactic-record) defines a fixed-point confidence ABI for the GNN→Chapel cross-FFI tactic-record contract. The module proves the total-order properties (reflexivity, antisymmetry) but explicitly defers two round-trip lemmas. The deferral requires an LTE-weakening step on the nat side that was intentionally left out as honest proof debt rather than closing with believe_me or assert_total. The file body documents this at lines 88-93 and 191-196.

Deferred lemmas

natToFinToNat : (n : Nat) -> (prf : LT n (S MaxConfidence)) -> finToNat (natToFinLT n {prf}) = n

clampRoundtripInRange : (n : Nat) -> (prf : LT n (S MaxConfidence)) -> finToNat (clampConfidence n) = n

Constraint

Zero believe_me, zero postulates, zero admits — same standard as the rest of src/abi/.

References

Filed via session 2026-05-30 TacticRecord landing arc.

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