Nuprl Lemma : singleton-type-product
∀[A,B:Type]. (singleton-type(A) ⇒ singleton-type(B) ⇒ singleton-type(A × B))
Proof
Definitions occuring in Statement :
singleton-type: singleton-type(A),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
singleton-type: singleton-type(A),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
all_wf,
equal_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
rename,
dependent_pairFormation,
independent_pairEquality,
hypothesisEquality,
cut,
hypothesis,
productEquality,
lemma_by_obid,
isectElimination,
lambdaEquality,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[A,B:Type]. (singleton-type(A) {}\mRightarrow{} singleton-type(B) {}\mRightarrow{} singleton-type(A \mtimes{} B))
Date html generated:
2016_05_14-PM-04_02_10
Last ObjectModification:
2015_12_26-PM-07_43_05
Theory : equipollence!!cardinality!
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