Nuprl Lemma : fun-equiv_wf
∀[X,A:Type]. ∀[E:A ⟶ A ⟶ ℙ]. ∀[f,g:X ⟶ A]. (fun-equiv(X;a,b.E[a;b];f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
fun-equiv: fun-equiv(X;a,b.E[a; b];f;g),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fun-equiv: fun-equiv(X;a,b.E[a; b];f;g),
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[X,A:Type]. \mforall{}[E:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. \mforall{}[f,g:X {}\mrightarrow{} A]. (fun-equiv(X;a,b.E[a;b];f;g) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_09_08
Last ObjectModification:
2015_12_26-AM-11_48_12
Theory : quot_1
Home
Index