Nuprl Lemma : predicate_equivalent_wf
∀[T:Type]. ∀[P1,P2:T ⟶ ℙ]. (P1 ⇐⇒ P2 ∈ ℙ)
Proof
Definitions occuring in Statement :
predicate_equivalent: P1 ⇐⇒ P2,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
predicate_equivalent: P1 ⇐⇒ P2,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
all_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[P1,P2:T {}\mrightarrow{} \mBbbP{}]. (P1 \mLeftarrow{}{}\mRightarrow{} P2 \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_05_42
Last ObjectModification:
2015_12_26-AM-11_32_38
Theory : relations
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