Nuprl Lemma : squash-product
∀[A,B:Type]. uiff(↓A × B;↓A × (↓B))
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
squash: ↓T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
squash: ↓T,
prop: ℙ
Lemmas referenced :
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
introduction,
cut,
productElimination,
thin,
independent_pairEquality,
sqequalHypSubstitution,
imageElimination,
hypothesis,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
baseClosed,
lemma_by_obid,
isectElimination,
productEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. uiff(\mdownarrow{}A \mtimes{} B;\mdownarrow{}A \mtimes{} (\mdownarrow{}B))
Date html generated:
2016_05_13-PM-04_14_02
Last ObjectModification:
2016_01_14-PM-07_28_50
Theory : subtype_1
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