Nuprl Lemma : rational-cube-complex_wf
∀[k,n:ℕ]. (n-dim-complex ∈ Type)
Proof
Definitions occuring in Statement :
rational-cube-complex: n-dim-complex,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s],
nat: ℕ,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
and: P ∧ Q,
rational-cube-complex: n-dim-complex,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
l_member_wf,
le_wf,
int_subtype_base,
istype-int,
lelt_wf,
set_subtype_base,
rat-cube-dimension_wf,
equal-wf-base,
l_all_wf2,
compatible-rat-cubes_wf,
pairwise_wf2,
no_repeats_wf,
rational-cube_wf,
list_wf
Rules used in proof :
isectIsTypeImplies,
isect_memberEquality_alt,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
setIsType,
because_Cache,
independent_isectElimination,
addEquality,
natural_numberEquality,
applyEquality,
rename,
setElimination,
intEquality,
universeIsType,
inhabitedIsType,
lambdaEquality_alt,
productEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k,n:\mBbbN{}]. (n-dim-complex \mmember{} Type)
Date html generated:
2019_10_29-AM-07_55_35
Last ObjectModification:
2019_10_17-PM-02_14_46
Theory : rationals
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