Nuprl Lemma : polymorphic-constant-base
∀[T:Type]. ∀f:Base ⟶ T. ∃t:T. ∀x:Base. ((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,
function: x:A ⟶ B[x],
base: Base,
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)↓,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
is-above: is-above(T;a;z),
cand: A c∧ B,
not: ¬A,
false: False
Lemmas referenced :
is-above_wf,
base_wf,
equal-wf-base,
all_wf,
equal_wf,
mono_wf,
value-type_wf,
bottom_diverge,
exception-not-bottom,
has-value_wf_base,
is-exception_wf,
sqle_wf_base,
and_wf
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,
dependent_pairFormation,
applyEquality,
functionExtensionality,
baseClosed,
functionEquality,
productEquality,
universeEquality,
pointwiseFunctionalityForEquality,
independent_functionElimination,
baseApply,
closedConclusion,
independent_pairFormation,
divergentSqle,
sqleRule,
sqleReflexivity,
voidElimination,
instantiate,
dependent_set_memberEquality,
applyLambdaEquality,
setElimination
Latex:
\mforall{}[T:Type]. \mforall{}f:Base {}\mrightarrow{} T. \mexists{}t:T. \mforall{}x:Base. ((f x) = t) supposing mono(T) \mwedge{} value-type(T)
Date html generated:
2018_05_21-PM-01_11_34
Last ObjectModification:
2018_05_01-PM-04_36_47
Theory : num_thy_1
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