Nuprl Lemma : sequence_subtype
∀[A,B:Type]. sequence(A) ⊆r sequence(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
sequence: sequence(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
nat: ℕ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
sequence: sequence(T)
Lemmas referenced :
subtype_rel_wf,
subtype_rel_dep_function,
int_seg_wf,
nat_wf,
subtype_rel_product
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
axiomEquality,
lambdaFormation,
independent_isectElimination,
because_Cache,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
functionEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[A,B:Type]. sequence(A) \msubseteq{}r sequence(B) supposing A \msubseteq{}r B
Date html generated:
2018_07_25-PM-01_29_34
Last ObjectModification:
2018_06_18-PM-10_51_19
Theory : arithmetic
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