Nuprl Lemma : has-interior-point_wf
∀[k:ℕ]. ∀[c,a:ℚCube(k)]. (has-interior-point(k;c;a) ∈ ℙ)
Proof
Definitions occuring in Statement :
has-interior-point: has-interior-point(k;c;a),
rational-cube: ℚCube(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,
has-interior-point: has-interior-point(k;c;a),
prop: ℙ,
exists: ∃x:A. B[x],
nat: ℕ,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
int_seg_wf,
rationals_wf,
rat-point-in-cube_wf,
rational-cube_wf,
rat-cube-face_wf,
equal_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c,a:\mBbbQ{}Cube(k)]. (has-interior-point(k;c;a) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-09_19_13
Last ObjectModification:
2019_11_02-PM-05_07_06
Theory : rationals
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