Nuprl Lemma : example3
∀[A,B,C:Type]. ((A ⇒ (B ∨ (A ⇒ C))) ⇒ A ⇒ (B ∨ C))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
member: t ∈ T,
guard: {T},
prop: ℙ
Lemmas referenced :
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
unionElimination,
inlFormation,
hypothesisEquality,
sqequalRule,
cut,
inrFormation,
functionEquality,
lemma_by_obid,
isectElimination,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. ((A {}\mRightarrow{} (B \mvee{} (A {}\mRightarrow{} C))) {}\mRightarrow{} A {}\mRightarrow{} (B \mvee{} C))
Date html generated:
2016_05_15-PM-07_21_43
Last ObjectModification:
2015_12_27-AM-11_26_19
Theory : general
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