Nuprl Lemma : poly-choice-eta-1
∀f:Base. ((∀x,y:Base. ((f x y) = y ∈ Base)) ⇒ (f ~ λx,y. y))
Proof
Definitions occuring in Statement :
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
base: Base,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
has-value: (a)↓,
or: P ∨ Q,
not: ¬A,
false: False,
top: Top
Lemmas referenced :
all_wf,
base_wf,
equal-wf-base,
subtype_base_sq,
subtype_rel_self,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
value-type-has-value,
int-value-type,
has-value_wf_base,
is-exception_wf,
sqle_wf_base,
not_id_sqle_bottom,
strictness-apply
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
instantiate,
cumulativity,
independent_isectElimination,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
because_Cache,
natural_numberEquality,
imageMemberEquality,
productElimination,
independent_functionElimination,
intEquality,
callbyvalueApply,
callbyvalueApplyCases,
unionElimination,
sqequalIntensionalEquality,
divergentSqle,
sqleReflexivity,
voidElimination,
sqleRule,
isect_memberEquality,
voidEquality
Latex:
\mforall{}f:Base. ((\mforall{}x,y:Base. ((f x y) = y)) {}\mRightarrow{} (f \msim{} \mlambda{}x,y. y))
Date html generated:
2018_05_21-PM-01_15_15
Last ObjectModification:
2018_05_01-PM-04_37_46
Theory : num_thy_1
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