Nuprl Lemma : example2
∀[A,B,C:Type]. (((A ⇒ B) ⇒ A) ⇒ (B ⇒ C) ⇒ (A ⇒ B) ⇒ (¬¬C))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
introduction,
lambdaEquality,
voidElimination,
functionEquality,
hypothesisEquality,
cut,
lemma_by_obid,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. (((A {}\mRightarrow{} B) {}\mRightarrow{} A) {}\mRightarrow{} (B {}\mRightarrow{} C) {}\mRightarrow{} (A {}\mRightarrow{} B) {}\mRightarrow{} (\mneg{}\mneg{}C))
Date html generated:
2016_05_15-PM-07_20_29
Last ObjectModification:
2015_12_27-AM-11_26_50
Theory : general
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