Nuprl Lemma : dl-equiv_wf
∀[phi,psi:Prop]. ((phi ⇐⇒ psi) ∈ ℙ')
Proof
Definitions occuring in Statement :
dl-equiv: (phi ⇐⇒ psi),
dl-prop: Prop,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dl-equiv: (phi ⇐⇒ psi),
prop: ℙ,
and: P ∧ Q
Lemmas referenced :
dl-valid_wf,
dl-implies_wf,
dl-prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[phi,psi:Prop]. ((phi \mLeftarrow{}{}\mRightarrow{} psi) \mmember{} \mBbbP{}')
Date html generated:
2019_10_15-AM-11_44_15
Last ObjectModification:
2019_03_27-AM-00_13_56
Theory : dynamic!logic
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