Nuprl Lemma : in-complex-boundary_wf
∀[k:ℕ]. ∀[f:ℚCube(k)]. ∀[K:ℚCube(k) List]. (in-complex-boundary(k;f;K) ∈ 𝔹)
Proof
Definitions occuring in Statement :
in-complex-boundary: in-complex-boundary(k;f;K),
rational-cube: ℚCube(k),
list: T List,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
all: ∀x:A. B[x],
in-complex-boundary: in-complex-boundary(k;f;K),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
list_wf,
l_member_wf,
is-rat-cube-face_wf,
filter_wf5,
rational-cube_wf,
length_wf,
isOdd_wf
Rules used in proof :
isectIsTypeImplies,
isect_memberEquality_alt,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
universeIsType,
inhabitedIsType,
setIsType,
rename,
setElimination,
dependent_functionElimination,
lambdaEquality_alt,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[f:\mBbbQ{}Cube(k)]. \mforall{}[K:\mBbbQ{}Cube(k) List]. (in-complex-boundary(k;f;K) \mmember{} \mBbbB{})
Date html generated:
2019_10_29-AM-07_58_09
Last ObjectModification:
2019_10_19-AM-11_06_13
Theory : rationals
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