matita/contribs/LOGIC/Weight/defs.ma

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  14
  15
  16
  17 (* PROOF WEIGHT
  18    For cut elimination and confluence
  19 *)
  20
  21 include "datatypes_defs/Context.ma".
  22
  23
  24 inductive Weight: Nat \to Context \to Proof \to Nat \to Prop \def
  25    | weight_prin: \forall Q,n,m. Weight m Q (prin n) m
  26    | weight_impw: \forall p,Q,m0,m1. Weight m0 Q p m1 \to
  27                   \forall m. (m1 + m0 == m) \to
  28                   Weight m0 Q (impw p) m
  29    | weight_impr: \forall p,Q,m0,m1. Weight m0 Q p m1 \to
  30                   \forall m. (m1 + m0 == m) \to
  31                   Weight m0 Q (impr p) m
  32    | weight_scut: \forall p1,Q,m0,m1. Weight (succ m0) Q p1 m1 \to
  33                   \forall p2,m2. Weight (succ m0) Q p2 m2 \to
  34                   \forall m. (m1 + m2 == m) \to
  35                   Weight m0 Q (scut p1 p2) m
  36 .