Nuprl Lemma : pair-blex_wf
∀[A,B:Type]. ∀[eq,Ra:A ⟶ A ⟶ 𝔹]. ∀[Rb:B ⟶ B ⟶ 𝔹]. (pair-blex(eq;Ra;Rb) ∈ (A × B) ⟶ (A × B) ⟶ 𝔹)
Proof
Definitions occuring in Statement :
pair-blex: pair-blex(eq;Ra;Rb),
bool: 𝔹,
uall: ∀[x:A]. B[x],
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,
pair-blex: pair-blex(eq;Ra;Rb),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
bor_wf,
pi1_wf,
band_wf,
pi2_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[eq,Ra:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbB{}]. \mforall{}[Rb:B {}\mrightarrow{} B {}\mrightarrow{} \mBbbB{}].
(pair-blex(eq;Ra;Rb) \mmember{} (A \mtimes{} B) {}\mrightarrow{} (A \mtimes{} B) {}\mrightarrow{} \mBbbB{})
Date html generated:
2016_05_13-PM-03_58_18
Last ObjectModification:
2015_12_26-AM-10_51_02
Theory : bool_1
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