Nuprl Lemma : truncate-map_wf
∀[X,Q:Type]. ∀f:X ⟶ ⇃(Q). (|f| ∈ ⇃(X) ⟶ ⇃(Q))
Proof
Definitions occuring in Statement :
truncate-map: |f|,
quotient: x,y:A//B[x; y],
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
true: True,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
true: True,
truncate-map: |f|
Lemmas referenced :
quotient_wf,
true_wf,
equiv_rel_true,
istype-universe,
half-squash-equality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
functionExtensionality,
pointwiseFunctionalityForEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
Error :lambdaEquality_alt,
hypothesis,
Error :inhabitedIsType,
Error :universeIsType,
independent_isectElimination,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
rename,
Error :equalityIsType1,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality,
Error :productIsType,
Error :equalityIsType4,
because_Cache,
Error :functionIsType,
axiomEquality,
Error :functionIsTypeImplies,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
instantiate,
universeEquality,
applyEquality
Latex:
\mforall{}[X,Q:Type]. \mforall{}f:X {}\mrightarrow{} \00D9(Q). (|f| \mmember{} \00D9(X) {}\mrightarrow{} \00D9(Q))
Date html generated:
2019_06_20-PM-00_32_50
Last ObjectModification:
2018_11_16-AM-11_47_43
Theory : quot_1
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