Nuprl Lemma : std-simplex_wf
∀[n:ℤ]. (Δ(n) ∈ Type)
Proof
Definitions occuring in Statement :
std-simplex: Δ(n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
std-simplex: Δ(n),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
all: ∀x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int_seg_wf,
real_wf,
rleq_wf,
int-to-real_wf,
req_wf,
rsum_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
setEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
addEquality,
hypothesisEquality,
hypothesis,
productEquality,
setElimination,
rename,
productElimination,
applyEquality,
lambdaEquality_alt,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbZ{}]. (\mDelta{}(n) \mmember{} Type)
Date html generated:
2019_10_30-AM-11_30_26
Last ObjectModification:
2019_07_31-PM-02_46_08
Theory : real!vectors
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