Nuprl Lemma : prod-discrete
∀A,B:Type. (discrete-type(A) ⇒ discrete-type(B) ⇒ discrete-type(A × B))
Proof
Definitions occuring in Statement :
discrete-type: discrete-type(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
product-discrete,
discrete-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
independent_functionElimination,
hypothesis,
because_Cache,
isectElimination,
universeEquality
Latex:
\mforall{}A,B:Type. (discrete-type(A) {}\mRightarrow{} discrete-type(B) {}\mRightarrow{} discrete-type(A \mtimes{} B))
Date html generated:
2018_05_22-PM-02_14_22
Last ObjectModification:
2017_10_29-PM-08_06_01
Theory : reals
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