Nuprl Lemma : polymorphic-constant-bool
∀f:⋂A:Type. (A ⟶ 𝔹). ∃t:𝔹. ∀A:Type. ∀x:A. f x = t
Proof
Definitions occuring in Statement :
bool: 𝔹,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
bool: 𝔹
Lemmas referenced :
polymorphic-constant,
bool_wf,
bool-mono,
union-value-type,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
independent_pairFormation,
sqequalRule,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
isectEquality,
universeEquality,
cumulativity,
functionEquality
Latex:
\mforall{}f:\mcap{}A:Type. (A {}\mrightarrow{} \mBbbB{}). \mexists{}t:\mBbbB{}. \mforall{}A:Type. \mforall{}x:A. f x = t
Date html generated:
2018_05_21-PM-01_11_44
Last ObjectModification:
2018_05_01-PM-04_36_54
Theory : num_thy_1
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