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fix(theories): make Dexcepted phoare bounds SMT-free #1149

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Merged
strub merged 1 commit into from
Oct 6, 2026
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fix(theories): make Dexcepted phoare bounds SMT-free #1149

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9 changes: 7 additions & 2 deletions theories/distributions/Dexcepted.ec
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Original file line number Diff line number Diff line change
Expand Up @@ -154,7 +154,10 @@ qed.
phoare phoare_indirect x' X' P:
[ S.indirect: x = x' /\ X = X' ==> P res ]
= (weight (dt x) * mu (dt x \ X x) P).
proof. bypr=> &m; smt(pr_indirect ge0_mu). qed.
proof.
bypr=> &m; rewrite mulr_ge0 1:ge0_weight 1:ge0_mu /= => [#] -> ->.
exact/(@pr_indirect &m x' X' P).
qed.

(* -------------------------------------------------------------------- *)
lemma ll_pr_indirect &m x' X' P:
Expand All @@ -166,7 +169,9 @@ phoare ll_phoare_indirect x' X' P:
[ S.indirect: x = x' /\ X = X' /\ is_lossless (dt x') ==> P res ]
= (mu (dt x \ X x) P).
proof.
by bypr=> &m; smt(ll_pr_indirect ge0_mu). qed.
bypr=> &m; rewrite ge0_mu /= => [#] -> -> dt_ll.
exact/(@ll_pr_indirect &m x' X' P dt_ll).
qed.

(* -------------------------------------------------------------------- *)
lemma indirect_direct &m x X P:
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