Nuprl Lemma : predicate-and_wf
∀[T,S:Type]. ∀[A:T ⟶ ℙ]. ∀[B:S ⟶ ℙ]. (predicate-and(A;B) ∈ (T × S) ⟶ ℙ)
Proof
Definitions occuring in Statement :
predicate-and: predicate-and(A;B),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
predicate-and: predicate-and(A;B),
prop: ℙ
Lemmas referenced :
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
spreadEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesis,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T,S:Type]. \mforall{}[A:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:S {}\mrightarrow{} \mBbbP{}]. (predicate-and(A;B) \mmember{} (T \mtimes{} S) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_08_59
Last ObjectModification:
2015_12_26-PM-07_54_48
Theory : fan-theorem
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