diff --git a/explicit/booleans.lp b/explicit/booleans.lp deleted file mode 100644 index 2d023db167dc8e9499e103268de5e675be08505e..0000000000000000000000000000000000000000 --- a/explicit/booleans.lp +++ /dev/null @@ -1,8 +0,0 @@ -require open pvs_cert explicit.pts_bindings - -definition bool ≔ Prop - -definition false ≔ prod Type Prop Prop uProp r (λ x : Term Type uProp, x) -definition true ≔ Term Prop false ⇒ Term Prop false - -definition bnot (P : Term Type uProp) ≔ Term Prop P ⇒ Term Prop false diff --git a/explicit/equalities.lp b/explicit/equalities.lp deleted file mode 100644 index ad267c7f1efeab3c8fff38708a91861419e851d4..0000000000000000000000000000000000000000 --- a/explicit/equalities.lp +++ /dev/null @@ -1,3 +0,0 @@ -require open pvs_cert explicit.pts_bindings explicit.booleans - -symbol eq (T : Term Kind uType) : Term Type T ⇒ Term Type T ⇒ Term Type uProp diff --git a/explicit/nat.lp b/explicit/nat.lp deleted file mode 100644 index dd2e3bc9af391702afda76c7b6eb5354ab43b642..0000000000000000000000000000000000000000 --- a/explicit/nat.lp +++ /dev/null @@ -1,8 +0,0 @@ -require open pvs_cert explicit.pts_bindings - -constant symbol int : Term Kind uType -symbol zero : Term Type int -injective symbol succ : Term Type int ⇒ Term Type int - -set builtin "0" ≔ zero -set builtin "+1" ≔ succ diff --git a/explicit/nat_ops.lp b/explicit/nat_ops.lp deleted file mode 100644 index 9ac3516064e3e708ea1cdd679f0ad1d68d0818a1..0000000000000000000000000000000000000000 --- a/explicit/nat_ops.lp +++ /dev/null @@ -1,12 +0,0 @@ -require open pvs_cert explicit.pts_bindings explicit.nat explicit.notequal - -symbol times : Term Type int ⇒ Term Type int ⇒ Term Type int -rule times &n 1 → &n - -set infix left 6 "*" ≔ times - -type λ x : Term Type int, neq int x 0 - -symbol prod_not_zero (x y : Term Type int) : - Term Prop (neq int x 0) ⇒ Term Prop (neq int y 0) ⇒ - Term Prop (neq int (x * y) 0) diff --git a/explicit/notequal.lp b/explicit/notequal.lp deleted file mode 100644 index 24df8b5b75b504d7e134c925bb24eb624776c101..0000000000000000000000000000000000000000 --- a/explicit/notequal.lp +++ /dev/null @@ -1,4 +0,0 @@ -require open pvs_cert explicit.pts_bindings explicit.booleans -require open explicit.equalities - -definition neq (T : Term Kind uType) (x y : Term Type T) ≔ bnot (eq T x y) diff --git a/explicit/pts_bindings.lp b/explicit/pts_bindings.lp deleted file mode 100644 index 9d4351a1114a7989d3d84ce21157aee1df44f592..0000000000000000000000000000000000000000 --- a/explicit/pts_bindings.lp +++ /dev/null @@ -1,7 +0,0 @@ -require open pvs_cert - -symbol r : Rule Type Prop Prop -symbol a : Axiom Prop Type - -definition uProp ≔ univ Prop Type I -definition uType ≔ univ Type Kind I diff --git a/explicit/rat.lp b/explicit/rat.lp deleted file mode 100644 index 6088674832c96ad11dff1f49724ecef1224654a8..0000000000000000000000000000000000000000 --- a/explicit/rat.lp +++ /dev/null @@ -1,17 +0,0 @@ -require open pvs_cert explicit.pts_bindings explicit.booleans explicit.equalities explicit.notequal - -constant symbol Nat : Term Kind uType -symbol Nz : Term Type Nat -symbol Nsuc : Term Type Nat ⇒ Term Type Nat - -constant symbol rat : Term Kind uType -constant symbol Qz : Term Type rat - -definition notzero ≔ psub uProp (λ x : Term Type uProp, x) - -symbol frac : Term Type Nat ⇒ ∀ m : Term Type notzero, Term Type rat - -symbol times : Term Type rat ⇒ Term Type rat ⇒ Term Type rat - -rule times (frac &A (pair &B &P)) (frac &C (pair &D &Q)) → - frac (Nat_times &A &C) (pair (Nat_times &B &D) (Nat_prod_not_zero &B &D &P &Q))