Nuprl Lemma : example1
∀[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],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
not: ¬A,
or: P ∨ Q,
false: False
Lemmas referenced :
false_wf,
or_wf,
not_wf,
minimal-double-negation-hyp-elim,
minimal-not-not-excluded-middle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
because_Cache,
universeEquality,
lambdaFormation,
functionEquality,
hypothesisEquality,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
independent_functionElimination,
unionElimination,
introduction,
lambdaEquality,
voidElimination
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_19_58
Last ObjectModification:
2015_12_27-AM-11_27_17
Theory : general
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