Section partial_soundness.
Existing Instance unit_kMD.
Context {P: ProgrammingLanguage}
{iP: ImperativeProgrammingLanguage P}
{MD: Model}
{R: Relation model}
{po_R: PreOrder Krelation}
{BSS: BigStepSemantics P model}
{iBSS: ImpBigStepSemantics P model BSS}.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{sepconL: SepconLanguage L}
{wandL: WandLanguage L}
{SM: Semantics L MD}
{kiSM: KripkeIntuitionisticSemantics L MD tt SM}
{kminSM: KripkeMinimumSemantics L MD tt SM}
{kpSM: KripkePropositionalSemantics L MD tt SM}.

Lemma hoare_while_partial_sound: forall b c B P,
(forall s, s |= B <-> eval_bool s b) ->
triple_partial_valid (P && B) c P ->
triple_partial_valid P (Swhile b c) (P && ~~ B).