Step
*
of Lemma
dl-valid-box-test-implies
∀phi,psi:Prop. (|= [(psi)?] phi
⇒ |= psi
⇒ phi)
BY
{ (((Auto THEN ParallelLast) THEN Auto)
THEN (InstHyp [⌜K⌝;⌜R⌝;⌜P⌝;⌜k⌝] (3)⋅ THEN Auto)
THEN All DlSemReduce
THEN Auto) }
Latex:
Latex:
\mforall{}phi,psi:Prop. (|= [(psi)?] phi {}\mRightarrow{} |= psi {}\mRightarrow{} phi)
By
Latex:
(((Auto THEN ParallelLast) THEN Auto)
THEN (InstHyp [\mkleeneopen{}K\mkleeneclose{};\mkleeneopen{}R\mkleeneclose{};\mkleeneopen{}P\mkleeneclose{};\mkleeneopen{}k\mkleeneclose{}] (3)\mcdot{} THEN Auto)
THEN All DlSemReduce
THEN Auto)
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