Nuprl Lemma : polymorphic-constant
∀[T:Type]. ∀f:⋂A:Type. (A ⟶ T). ∃t:T. ∀A:Type. ∀x:A. ((f x) = t ∈ T) supposing mono(T) ∧ value-type(T)
Proof
Definitions occuring in Statement :
mono: mono(T),
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
apply: f a,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
and: P ∧ Q,
mono: mono(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
value-type: value-type(T),
has-value: (a)↓,
cand: A c∧ B,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
is-above_wf,
base_wf,
equal-wf-base,
polymorphic-constant-base,
all_wf,
equal_wf,
mono_wf,
value-type_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
axiomEquality,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
isect_memberEquality,
axiomSqleEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
rename,
lambdaFormation,
independent_isectElimination,
independent_pairFormation,
dependent_pairFormation,
universeEquality,
instantiate,
applyEquality,
isectEquality,
functionEquality,
productEquality,
pointwiseFunctionalityForEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}f:\mcap{}A:Type. (A {}\mrightarrow{} T). \mexists{}t:T. \mforall{}A:Type. \mforall{}x:A. ((f x) = t) supposing mono(T) \mwedge{} value-type(T)
Date html generated:
2017_10_01-AM-09_07_24
Last ObjectModification:
2017_07_26-PM-04_46_47
Theory : general
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