Nuprl Lemma : immediate-rc-face_wf
∀[k:ℕ]. ∀[f,c:ℚCube(k)]. (immediate-rc-face(k;f;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
immediate-rc-face: immediate-rc-face(k;f;c),
rational-cube: ℚCube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s],
nat: ℕ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
immediate-rc-face: immediate-rc-face(k;f;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
subtract_wf,
int_subtype_base,
istype-int,
lelt_wf,
set_subtype_base,
rat-cube-dimension_wf,
equal-wf-base,
rat-cube-face_wf
Rules used in proof :
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
axiomEquality,
equalitySymmetry,
equalityTransitivity,
inhabitedIsType,
independent_isectElimination,
rename,
setElimination,
addEquality,
natural_numberEquality,
lambdaEquality_alt,
applyEquality,
intEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[f,c:\mBbbQ{}Cube(k)]. (immediate-rc-face(k;f;c) \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-07_53_48
Last ObjectModification:
2019_10_17-PM-02_57_10
Theory : rationals
Home
Index