Nuprl Lemma : minimal-not-not-implies
∀[P,A:ℙ]. (((((P ⇒ A) ⇒ A) ⇒ (P ∨ A)) ⇒ A) ⇒ A)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
or: P ∨ Q,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
or_wf,
minimal-not-not-xmiddle
Rules used in proof :
unionElimination,
inlFormation,
inrFormation,
sqequalRule,
functionEquality,
independent_functionElimination,
hypothesis,
lambdaFormation,
universeEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[P,A:\mBbbP{}]. (((((P {}\mRightarrow{} A) {}\mRightarrow{} A) {}\mRightarrow{} (P \mvee{} A)) {}\mRightarrow{} A) {}\mRightarrow{} A)
Date html generated:
2018_05_24-PM-02_14_27
Last ObjectModification:
2018_05_23-PM-01_49_49
Theory : core_2
Home
Index