Nuprl Lemma : canonicalizable-set
∀[T:Type]. ∀[B:T ⟶ Type]. (canonicalizable(T) ⇒ canonicalizable({x:T| B[x]} ))
Proof
Definitions occuring in Statement :
canonicalizable: canonicalizable(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
canonicalizable: canonicalizable(T),
exists: ∃x:A. B[x],
member: t ∈ T,
so_apply: x[s],
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
iff_weakening_equal,
equal_wf,
canonicalizable_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation_alt,
functionExtensionality,
applyEquality,
hypothesisEquality,
setElimination,
rename,
cut,
hypothesis,
setEquality,
dependent_functionElimination,
introduction,
extract_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
independent_functionElimination,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
imageElimination,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeIsType,
setIsType,
functionIsType,
equalityIstype,
sqequalBase,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[B:T {}\mrightarrow{} Type]. (canonicalizable(T) {}\mRightarrow{} canonicalizable(\{x:T| B[x]\} ))
Date html generated:
2020_05_19-PM-09_35_49
Last ObjectModification:
2020_01_04-PM-07_56_39
Theory : call!by!value_2
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