Nuprl Lemma : polymorphic-constant-bool
āf:āA:Type. (A ā¶ š¹). āt:š¹. āA:Type. āx:A. f x = t
Proof
Definitions occuring in Statement :
bool: š¹,
all: āx:A. B[x],
exists: āx:A. B[x],
apply: f a,
isect: āx:A. B[x],
function: x:A ā¶ B[x],
universe: Type,
equal: s = t ā T
Definitions unfolded in proof :
all: āx:A. B[x],
uall: ā[x:A]. B[x],
member: t ā T,
uimplies: b supposing a,
and: P ā§ Q,
cand: A cā§ B,
bool: š¹
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:
2016_05_15-PM-03_15_33
Last ObjectModification:
2015_12_27-PM-01_02_55
Theory : general
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