Nuprl Lemma : function-discrete
∀A:Type. ∀B:A ⟶ Type. ((∀a:A. discrete-type(B[a])) ⇒ discrete-type(a:A ⟶ B[a]))
Proof
Definitions occuring in Statement :
discrete-type: discrete-type(T),
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
discrete-type: discrete-type(T),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
real_wf,
all_wf,
req_wf,
equal_wf,
discrete-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
functionExtensionality,
hypothesisEquality,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
functionEquality,
cumulativity,
applyEquality,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}A:Type. \mforall{}B:A {}\mrightarrow{} Type. ((\mforall{}a:A. discrete-type(B[a])) {}\mRightarrow{} discrete-type(a:A {}\mrightarrow{} B[a]))
Date html generated:
2018_05_22-PM-02_14_36
Last ObjectModification:
2017_10_29-PM-07_38_10
Theory : reals
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