Nuprl Lemma : detach_fun_wf
∀[T:Type]. ∀[A:T ⟶ ℙ]. (detach_fun(T;A) ∈ Type)
Proof
Definitions occuring in Statement :
detach_fun: detach_fun(T;A),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
detach_fun: detach_fun(T;A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
bool_wf,
all_wf,
iff_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
setEquality,
functionEquality,
hypothesisEquality,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[A:T {}\mrightarrow{} \mBbbP{}]. (detach\_fun(T;A) \mmember{} Type)
Date html generated:
2016_05_15-PM-00_00_22
Last ObjectModification:
2015_12_26-PM-11_26_51
Theory : gen_algebra_1
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