Nuprl Lemma : adjacent-cubes_wf
∀[k:ℕ]. ∀[c1,c2:real-cube(k)]. (adjacent-cubes(k;c1;c2) ∈ ℙ)
Proof
Definitions occuring in Statement :
adjacent-cubes: adjacent-cubes(k;c1;c2),
real-cube: real-cube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
adjacent-cubes: adjacent-cubes(k;c1;c2),
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
all: ∀x:A. B[x],
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
or: P ∨ Q
Lemmas referenced :
exists_wf,
int_seg_wf,
all_wf,
not_wf,
equal-wf-base,
req_wf,
cube-lower_wf,
cube-upper_wf,
or_wf,
subtype_rel_self,
real_wf,
real-cube_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality_alt,
productEquality,
functionEquality,
applyEquality,
hypothesisEquality,
inhabitedIsType,
productElimination,
imageElimination,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c1,c2:real-cube(k)]. (adjacent-cubes(k;c1;c2) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-11_31_36
Last ObjectModification:
2019_09_27-PM-01_35_30
Theory : real!vectors
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