Nuprl Lemma : double-negation-iff-xmiddle
∀[A:Type]. (∀[P:ℙ]. (((P ⇒ A) ⇒ A) ⇒ (P ∨ A)) ⇐⇒ ∀[P:ℙ]. (P ∨ (P ⇒ A)))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
or: P ∨ Q,
guard: {T}
Lemmas referenced :
uall_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
universeEquality,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
lambdaEquality,
cumulativity,
functionEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
inrFormation,
inlFormation,
because_Cache,
unionElimination
Latex:
\mforall{}[A:Type]. (\mforall{}[P:\mBbbP{}]. (((P {}\mRightarrow{} A) {}\mRightarrow{} A) {}\mRightarrow{} (P \mvee{} A)) \mLeftarrow{}{}\mRightarrow{} \mforall{}[P:\mBbbP{}]. (P \mvee{} (P {}\mRightarrow{} A)))
Date html generated:
2016_05_15-PM-03_19_06
Last ObjectModification:
2015_12_27-PM-01_03_47
Theory : general
Home
Index