Nuprl Lemma : rev_implies_weakening_rev_uimplies
∀[P,Q:ℙ]. (rev_uimplies(P;Q) ⇒ {P ⇐ Q})
Proof
Definitions occuring in Statement :
rev_uimplies: rev_uimplies(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
member: t ∈ T,
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a
Lemmas referenced :
rev_uimplies_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[P,Q:\mBbbP{}]. (rev\_uimplies(P;Q) {}\mRightarrow{} \{P \mLeftarrow{}{} Q\})
Date html generated:
2019_06_20-AM-11_14_05
Last ObjectModification:
2018_09_26-AM-10_41_46
Theory : core_2
Home
Index