Nuprl Lemma : no-uniform-Peirce's-law
¬(∀[P,B:ℙ]. (((P ⇒ B) ⇒ P) ⇒ P))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
false: False
Lemmas referenced :
Peirce's-law-iff-xmiddle,
no-uniform-xmiddle,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
productElimination,
thin,
independent_functionElimination,
hypothesis,
sqequalRule,
isectIsType,
universeIsType,
universeEquality,
inhabitedIsType,
hypothesisEquality,
functionIsType,
because_Cache,
isect_memberFormation_alt,
voidElimination,
isectElimination
Latex:
\mneg{}(\mforall{}[P,B:\mBbbP{}]. (((P {}\mRightarrow{} B) {}\mRightarrow{} P) {}\mRightarrow{} P))
Date html generated:
2019_10_15-AM-11_06_38
Last ObjectModification:
2019_06_26-PM-04_18_13
Theory : general
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