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nx_classical.nx

buildroot/runtime/nx_classical.nx

2156 B52 linesdepth 6pulls 6 transitivereach 1 importersview sourcekind librarytopic classical
docsdependenciesstructsconstsfunctions

about

nx_classical.nx -- classical-logic axioms. Closes the named blocker for nonconstructive proofs (currently PARTIAL in the audit). Per user 2026-05-15: "no losses". Adds two axioms that are sound in CLASSICAL but not INTUITIONISTIC logic. The kernel core (nx_kernel_v2) stays intuitionistic; classical proofs explicitly cite these axioms so the audit trail always shows whether classical logic was used. LEM: for any A, A | ~A DNE: for any A, ~~A => A LEM and DNE are interderivable in classical logic; we ship both because each saves a step in different proof shapes. HOL Light derives the rest from these (Peirce's law, RAA, etc.) via the engine + the existing v2 rules.

dependencies 1 imports · 1 importers

nx_kernel_v2.nx nx_classical.nx nx_world_class_test.nx

imports: nx_kernel_v2.nx

imported by: nx_world_class_test.nx

structs

none

consts

none

functions

28func nx_classical_lem(ch: *K2Chain, a: *Term) -> nx_int
33func nx_classical_dne(ch: *K2Chain, a: *Term) -> nx_int
40func nx_classical_peirce(ch: *K2Chain, a: *Term, b: *Term) -> nx_int
47func nx_classical_register_basics(ch: *K2Chain, a: *Term, b: *Term) -> nx_int