Nuprl Lemma : polymorphic-choice-base-sq
∀f:Base. ((f ∈ ⋂A:Type. (A ⟶ A ⟶ A)) ⇒ ((f ~ λx.if f x is lambda then λy.x otherwise ⊥) ∨ (f ~ λx,y. y)))
Proof
Definitions occuring in Statement :
bottom: ⊥,
islambda: if z is lambda then a otherwise b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
member: t ∈ T,
apply: f a,
lambda: λx.A[x],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
base: Base,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
or: P ∨ Q,
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
polymorphic-choice-base,
equal-wf-base,
base_wf,
poly-choice-eta-2,
poly-choice-eta-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
equalityTransitivity,
hypothesis,
equalitySymmetry,
unionElimination,
inlFormation,
sqequalIntensionalEquality,
hypothesisEquality,
baseClosed,
sqequalRule,
inrFormation,
baseApply,
closedConclusion,
instantiate,
isectElimination,
isectEquality,
universeEquality,
cumulativity,
functionEquality,
because_Cache,
independent_functionElimination
Latex:
\mforall{}f:Base
((f \mmember{} \mcap{}A:Type. (A {}\mrightarrow{} A {}\mrightarrow{} A)) {}\mRightarrow{} ((f \msim{} \mlambda{}x.if f x is lambda then \mlambda{}y.x otherwise \mbot{}) \mvee{} (f \msim{} \mlambda{}x,y. y))\000C)
Date html generated:
2018_05_21-PM-01_16_12
Last ObjectModification:
2018_05_01-PM-04_37_58
Theory : num_thy_1
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