Nuprl Lemma : dl-logical-eq-weak_wf
∀[a,b:Prog]. ((a ⇐⇒w b) ∈ ℙ')
Proof
Definitions occuring in Statement :
dl-logical-eq-weak: (a ⇐⇒w b),
dl-prog: Prog,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dl-logical-eq-weak: (a ⇐⇒w b),
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
all: ∀x:A. B[x]
Lemmas referenced :
nat_wf,
not_wf,
l_member_wf,
dl-prop-atoms_wf,
dl-prog-obj_wf,
dl-valid_wf,
dl-implies_wf,
dl-diamond_wf,
dl-aprop_wf,
dl-prog_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
cumulativity,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[a,b:Prog]. ((a \mLeftarrow{}{}\mRightarrow{}w b) \mmember{} \mBbbP{}')
Date html generated:
2019_10_15-AM-11_45_57
Last ObjectModification:
2019_03_26-PM-00_11_57
Theory : dynamic!logic
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