Nuprl Lemma : tunion-valueall-type
∀[A:Type]. ∀[B:A ⟶ Type]. valueall-type(⋃a:A.B[a]) supposing ∀a:A. valueall-type(B[a])
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
uimplies: b supposing a,
tunion: ⋃x:A.B[x],
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
valueall-type: valueall-type(T),
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
tunion: ⋃x:A.B[x],
has-value: (a)↓,
has-valueall: has-valueall(a),
so_apply: x[s],
so_lambda: λ2x.t[x],
top: Top,
pi1: fst(t),
prop: ℙ,
squash: ↓T,
guard: {T}
Lemmas referenced :
sq_stable__has-value,
valueall-type-has-valueall,
pi1_wf,
pi2_wf,
top_wf,
equal_wf,
equal-wf-base,
tunion_wf,
base_wf,
all_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
hypothesis,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lambdaFormation,
imageElimination,
applyEquality,
functionExtensionality,
cumulativity,
lambdaEquality,
productElimination,
dependent_pairEquality,
independent_isectElimination,
independent_pairEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productEquality,
dependent_functionElimination,
imageMemberEquality,
axiomSqleEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. valueall-type(\mcup{}a:A.B[a]) supposing \mforall{}a:A. valueall-type(B[a])
Date html generated:
2017_04_14-AM-07_15_04
Last ObjectModification:
2017_02_27-PM-02_50_42
Theory : call!by!value_1
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