for @{ λ${ident a} : S $A. $P }.
notation "'I'" non associative with precedence 90 for @{'I}.
-interpretation "I" 'I = (I_ _).
+interpretation "I" 'I = (I_ ?).
notation < "'I' \lpar a \rpar" non associative with precedence 90 for @{'I1 $a}.
-interpretation "I a" 'I1 a = (I_ _ a).
+interpretation "I a" 'I1 a = (I_ ? a).
notation "'C'" non associative with precedence 90 for @{'C}.
-interpretation "C" 'C = (C_ _).
+interpretation "C" 'C = (C_ ?).
notation < "'C' \lpar a \rpar" non associative with precedence 90 for @{'C1 $a}.
-interpretation "C a" 'C1 a = (C_ _ a).
+interpretation "C a" 'C1 a = (C_ ? a).
notation < "'C' \lpar a , i \rpar" non associative with precedence 90 for @{'C2 $a $i}.
-interpretation "C a i" 'C2 a i = (C_ _ a i).
+interpretation "C a i" 'C2 a i = (C_ ? a i).
definition in_subset :=
λA:AxiomSet.λa∈A.λU:Ω^A.content A U a.
notation "hvbox(a break εU)" non associative with precedence 50 for
@{'in_subset $a $U}.
-interpretation "In subset" 'in_subset a U = (in_subset _ a U).
+interpretation "In subset" 'in_subset a U = (in_subset ? a U).
definition for_all ≝ λA:AxiomSet.λU:Ω^A.λP:A → CProp.∀x.xεU → P x.
| infinity_ : ∀a.∀i : I a. for_all A (C a i) (covers A U) → covers A U a.
notation "'refl'" non associative with precedence 90 for @{'refl}.
-interpretation "refl" 'refl = (refl_ _ _ _).
+interpretation "refl" 'refl = (refl_ ? ? ?).
notation "'infinity'" non associative with precedence 90 for @{'infinity}.
-interpretation "infinity" 'infinity = (infinity_ _ _ _).
+interpretation "infinity" 'infinity = (infinity_ ? ? ?).
notation "U ⊲ V" non associative with precedence 45
for @{ 'covers_subsets $U $V}.
-interpretation "Covers subsets" 'covers_subsets U V = (for_all _ U (covers _ V)).
-interpretation "Covers elem subset" 'covers_subsets U V = (covers _ V U).
+interpretation "Covers subsets" 'covers_subsets U V = (for_all ? U (covers ? V)).
+interpretation "Covers elem subset" 'covers_subsets U V = (covers ? V U).
definition subseteq := λA:AxiomSet.λU,V:Ω^A.∀x.xεU → xεV.
-interpretation "subseteq" 'subseteq u v = (subseteq _ u v).
+interpretation "subseteq" 'subseteq u v = (subseteq ? u v).
definition covers_elim_ ≝
in
aux.
-interpretation "char" 'subset p = (mk_powerset _ p).
+interpretation "char" 'subset p = (mk_powerset ? p).
definition covers_elim :
∀A:AxiomSet.∀U: Ω^A.∀P:A→CProp.∀H1: U ⊆ {x | P x}.
qed.
notation "'trans'" non associative with precedence 90 for @{'trans}.
-interpretation "trans" 'trans = (trans_ _ _).
+interpretation "trans" 'trans = (trans_ ? ?).