Nuprl Lemma : ctt-type-meaning-subtype
∀[X:⊢''']. (cttType(X) ⊆r ctt-type-meaning1{i:l}(X))
Proof
Definitions occuring in Statement :
ctt-type-meaning: cttType(X),
ctt-type-meaning1: ctt-type-meaning1{i:l}(X),
cubical_set: CubicalSet,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
ctt-type-meaning: cttType(X),
all: ∀x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
btrue: tt,
ctt-type-meaning1: ctt-type-meaning1{i:l}(X),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
ctt-level-type: {X ⊢lvl _},
cubical-type: {X ⊢ _},
nat: ℕ,
less_than: a < b,
squash: ↓T,
bfalse: ff
Lemmas referenced :
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-le,
istype-less_than,
ctt-level-type_wf,
intformand_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_term_value_var_lemma,
istype-top,
int_seg_subtype_special,
int_seg_cases,
ctt-type-meaning_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaEquality_alt,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
unionElimination,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
sqequalRule,
dependent_pairEquality_alt,
dependent_set_memberEquality_alt,
independent_pairFormation,
approximateComputation,
dependent_pairFormation_alt,
Error :memTop,
universeIsType,
voidElimination,
productIsType,
independent_pairEquality,
imageElimination,
int_eqEquality,
hypothesis_subsumption
Latex:
\mforall{}[X:\mvdash{}''']. (cttType(X) \msubseteq{}r ctt-type-meaning1\{i:l\}(X))
Date html generated:
2020_05_20-PM-07_59_21
Last ObjectModification:
2020_05_05-AM-09_42_57
Theory : cubical!type!theory
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