- mq: reflexive … (sq M);
- mr: replace_2 … (sq M) (sq M) (sq M);
- mc: compatible_3 … (ap M) (sq M) (sq M) (sq M);
- ms: ∀gv,lv,s. ⟦⋆s⟧{M}[gv, lv] ≗ sv M s;
- ml: ∀gv,lv,i. ⟦#i⟧{M}[gv, lv] ≗ lv i;
- mg: ∀gv,lv,l. ⟦§l⟧{M}[gv, lv] ≗ gv l;
- md: ∀gv,lv,p,V,T. ⟦ⓓ{p}V.T⟧{M}[gv, lv] ≗ ⟦T⟧[gv, ⫯[⟦V⟧[gv, lv]]lv];
- mi: ∀gv,lv1,lv2,p,W,T. ⟦W⟧{M}[gv, lv1] ≗ ⟦W⟧{M}[gv, lv2] →
- (∀d. ⟦T⟧{M}[gv, ⫯[d]lv1] ≗ ⟦T⟧{M}[gv, ⫯[d]lv2]) →
- ⟦ⓛ{p}W.T⟧[gv, lv1] ≗ ⟦ⓛ{p}W.T⟧[gv, lv2];
- ma: ∀gv,lv,V,T. ⟦ⓐV.T⟧{M}[gv, lv] ≗ ⟦V⟧[gv, lv] @ ⟦T⟧[gv, lv];
- me: ∀gv,lv,W,T. ⟦ⓝW.T⟧{M}[gv, lv] ≗ ⟦T⟧[gv, lv];
- mb: ∀gv,lv,d,p,W,T. d @ ⟦ⓛ{p}W.T⟧{M}[gv, lv] ≗ ⟦T⟧[gv, ⫯[d]lv]
+(* Note: equivalence: reflexivity *)
+ mr: reflexive … (sq M);
+(* Note: equivalence: compatibility *)
+ mq: replace_2 … (sq M) (sq M) (sq M);
+(* Note: conjunction: compatibility *)
+ mc: ∀p. compatible_3 … (co M p) (sq M) (sq M) (sq M);
+(* Note: application: compatibility *)
+ mp: compatible_3 … (ap M) (sq M) (sq M) (sq M);
+(* Note: interpretation: sort *)
+ ms: ∀gv,lv,s. ⟦⋆s⟧{M}[gv,lv] ≗ sv M s;
+(* Note: interpretation: local reference *)
+ ml: ∀gv,lv,i. ⟦#i⟧{M}[gv,lv] ≗ lv i;
+(* Note: interpretation: global reference *)
+ mg: ∀gv,lv,l. ⟦§l⟧{M}[gv,lv] ≗ gv l;
+(* Note: interpretation: intensional binder *)
+ mi: ∀p,gv1,gv2,lv1,lv2,W,T. ⟦W⟧{M}[gv1,lv1] ≗ ⟦W⟧{M}[gv2,lv2] →
+ (∀d. ⟦T⟧{M}[gv1,⫯[0←d]lv1] ≗ ⟦T⟧{M}[gv2,⫯[0←d]lv2]) →
+ ⟦ⓛ[p]W.T⟧[gv1,lv1] ≗ ⟦ⓛ[p]W.T⟧[gv2,lv2];
+(* Note: interpretation: abbreviation *)
+ md: ∀p,gv,lv,V,T. ⟦ⓓ[p]V.T⟧{M}[gv,lv] ≗ ⟦V⟧[gv,lv] ⊕[p] ⟦T⟧[gv,⫯[0←⟦V⟧[gv,lv]]lv];
+(* Note: interpretation: application *)
+ ma: ∀gv,lv,V,T. ⟦ⓐV.T⟧{M}[gv,lv] ≗ ⟦V⟧[gv,lv] @ ⟦T⟧[gv,lv];
+(* Note: interpretation: ζ-equivalence *)
+ mz: ∀d1,d2. d1 ⊕{M}[Ⓣ] d2 ≗ d2;
+(* Note: interpretation: ϵ-equivalence *)
+ me: ∀gv,lv,W,T. ⟦ⓝW.T⟧{M}[gv,lv] ≗ ⟦T⟧[gv,lv];
+(* Note: interpretation: β-requivalence *)
+ mb: ∀p,gv,lv,d,W,T. d @ ⟦ⓛ[p]W.T⟧{M}[gv,lv] ≗ d ⊕[p] ⟦T⟧[gv,⫯[0←d]lv];
+(* Note: interpretation: θ-requivalence *)
+ mh: ∀p,d1,d2,d3. d1 @ (d2 ⊕{M}[p] d3) ≗ d2 ⊕[p] (d1 @ d3)