Nuprl Lemma : CCC-product
∀A,B:Type. (CCC(A) ⇒ CCC(B) ⇒ CCC(A × B))
Proof
Definitions occuring in Statement :
contra-cc: CCC(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
prop: ℙ,
member: t ∈ T,
contra-cc: CCC(T),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
istype-universe,
contra-cc_wf,
subtype_rel_self,
istype-nat
Rules used in proof :
rename,
Error :inhabitedIsType,
universeEquality,
isectElimination,
instantiate,
because_Cache,
Error :productIsType,
Error :dependent_pairFormation_alt,
productElimination,
Error :functionIsType,
independent_functionElimination,
hypothesis,
extract_by_obid,
introduction,
cut,
Error :universeIsType,
independent_pairEquality,
applyEquality,
hypothesisEquality,
functionEquality,
sqequalRule,
Error :lambdaEquality_alt,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}A,B:Type. (CCC(A) {}\mRightarrow{} CCC(B) {}\mRightarrow{} CCC(A \mtimes{} B))
Date html generated:
2019_06_20-PM-03_01_05
Last ObjectModification:
2019_06_12-PM-09_16_49
Theory : continuity
Home
Index