Nuprl Lemma : interval-vec_wf
∀[I:Interval]. ∀[n:ℕ]. (I^n ∈ Type)
Proof
Definitions occuring in Statement :
interval-vec: I^n,
interval: Interval,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
real-vec: ℝ^n,
so_lambda: λ2x.t[x],
nat: ℕ,
interval-vec: I^n,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
interval_wf,
nat_wf,
i-member_wf,
int_seg_wf,
all_wf,
real-vec_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
applyEquality,
lambdaEquality,
rename,
setElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:Interval]. \mforall{}[n:\mBbbN{}]. (I\^{}n \mmember{} Type)
Date html generated:
2018_07_29-AM-09_44_48
Last ObjectModification:
2018_07_02-AM-11_13_44
Theory : reals
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