Nuprl Lemma : not-not-A-B-example
∀[A,B,F:ℙ]. ((((A ∧ B) ∨ (A ⇒ F) ∨ (B ⇒ F)) ⇒ F) ⇒ F)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
or: P ∨ Q,
and: P ∧ Q
Lemmas referenced :
or_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
thin,
functionEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
universeEquality,
inrFormation,
inlFormation,
independent_pairFormation
Latex:
\mforall{}[A,B,F:\mBbbP{}]. ((((A \mwedge{} B) \mvee{} (A {}\mRightarrow{} F) \mvee{} (B {}\mRightarrow{} F)) {}\mRightarrow{} F) {}\mRightarrow{} F)
Date html generated:
2016_05_15-PM-03_19_00
Last ObjectModification:
2015_12_27-PM-01_03_50
Theory : general
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