ABI Layer 3: (Trit, and3) is a commutative idempotent meet-semilattice#40
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Flagship semantic proof: negation involution + De Morgan laws, plus a decidable `Designated` (classical-truth) proposition with sound+complete Dec, certifier soundness, conjunction preservation, and positive + negative controls (negation is provably not the identity; U/F are provably not designated). Verified with idris2 0.7.0 (build clean, zero warnings) + adversarial false-proof rejection. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
…er the Kleene order Adds Betlangiser.ABI.Invariants, a second, deeper machine-checked theorem built over the existing Semantics model (Trit/and3/or3), distinct from the Layer-2 doubleNeg/De Morgan laws: - and3Comm, and3Assoc (full 27-case), and3Idem — the semilattice laws; - Leq3, the Kleene information order F <= U <= T, with reflexivity, transitivity, and a sound+complete decision procedure decLeq3; - and3LowerL/R + and3Greatest proving and3 is the meet (GLB) for Leq3; - positive controls (inhabited witnesses) and negative/non-vacuity controls (tNotLeqU, andUUNotTop, topNotBelowMeetTF). No believe_me/postulate/assert/sorry. %default total. Adversarially verified: a false `Leq3 T U` is rejected by the type checker. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Signed-off-by: Jonathan D.A. Jewell <6759885+hyperpolymath@users.noreply.github.com>
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Summary
Layer 3 (second, deeper invariant): proves
(Trit, and3)is a commutative, associative, idempotent meet-semilattice whose induced order matches the Kleene truth order. Distinct from and deeper than the Layer-2 double-negation/De Morgan laws.New module
Betlangiser.ABI.Invariants(imports the Layer-2Semanticsmodel). Positive + non-vacuity controls.Testing
Idris2 0.7.0
--build→ exit 0, zero warnings. Adversarial rejection confirmed.build/removed. Nobelieve_me/postulate/sorry.🤖 Generated with Claude Code
https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Generated by Claude Code