Nuprl Lemma : base-member-per-function
∀[A:Type]. ∀[B:per-function(A;x.Type)]. ∀[f:Base].
f ∈ per-function(A;x.B[x]) supposing ∀[a,a':Base]. (f a) = (f a') ∈ B[a] supposing a = a' ∈ A
Proof
Definitions occuring in Statement :
per-function: per-function(A;a.B[a]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
apply: f a,
base: Base,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-function: type-function{i:l}(A),
uimplies: b supposing a,
function-eq: function-eq(A;a.B[a];f;g),
per-function: per-function(A;a.B[a])
Lemmas referenced :
per-function_wf_type,
per-function-type-apply,
per-function_wf,
istype-universe,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
sqequalRule,
Error :isectIsType,
Error :inhabitedIsType,
Error :equalityIsType4,
hypothesis,
equalityTransitivity,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
Error :universeIsType,
universeEquality,
pertypeMemberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:per-function(A;x.Type)]. \mforall{}[f:Base].
f \mmember{} per-function(A;x.B[x]) supposing \mforall{}[a,a':Base]. (f a) = (f a') supposing a = a'
Date html generated:
2019_06_20-AM-11_30_03
Last ObjectModification:
2018_10_06-AM-09_00_31
Theory : per!type
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