Nuprl Lemma : cube-face_wf
∀[k:ℕ]. ∀[i:ℕk]. ∀[up:𝔹]. ∀[c:real-cube(k)]. (cube-face(i;up;c) ∈ real-cube(k))
Proof
Definitions occuring in Statement :
cube-face: cube-face(i;up;c),
real-cube: real-cube(k),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-cube: real-cube(k),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
cube-face: cube-face(i;up;c),
ifthenelse: if b then t else f fi ,
real-vec: ℝ^n,
int_seg: {i..j-},
bfalse: ff,
nat: ℕ
Lemmas referenced :
ifthenelse_wf,
eq_int_wf,
real_wf,
real-cube_wf,
bool_wf,
int_seg_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
independent_pairEquality,
lambdaEquality_alt,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
inhabitedIsType,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
natural_numberEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[i:\mBbbN{}k]. \mforall{}[up:\mBbbB{}]. \mforall{}[c:real-cube(k)]. (cube-face(i;up;c) \mmember{} real-cube(k))
Date html generated:
2019_10_30-AM-11_32_01
Last ObjectModification:
2019_09_27-PM-01_49_52
Theory : real!vectors
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