Nuprl Lemma : example1-ext
∀[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 :
member: t ∈ T,
example1,
minimal-double-negation-hyp-elim,
minimal-not-not-excluded-middle
Lemmas referenced :
example1,
minimal-double-negation-hyp-elim,
minimal-not-not-excluded-middle
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
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:
2018_05_21-PM-08_54_56
Last ObjectModification:
2018_05_19-PM-05_07_18
Theory : general
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