Nuprl Lemma : ctt_meaning_functionality
∀[ctxt:?CubicalContext]. ∀[t,t':CttTerm]. [[ctxt;t]] = [[ctxt;t']] ∈ 𝕌{i'''''} supposing ctt-eq{i:l}(t;t')
Proof
Definitions occuring in Statement :
ctt_meaning: [[ctxt;t]],
ctt-eq: ctt-eq{i:l}(a;b),
ctt-term: CttTerm,
cubical-context: ?CubicalContext,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ctt_meaning: [[ctxt;t]],
prop: ℙ,
squash: ↓T,
true: True,
ctt-eq: ctt-eq{i:l}(a;b),
guard: {T},
ctt-term: CttTerm,
wfterm: wfterm(opr;sort;arity),
ctt-meaning-type: ctt-meaning-type{i:l}(X;t),
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
less_than': less_than'(a;b)
Lemmas referenced :
context-ok_wf,
squash_wf,
true_wf,
istype-universe,
ctt-eq_wf,
isvarterm_wf,
ctt-op_wf,
isvarterm_functionality,
subtype_base_sq,
bool_wf,
bool_subtype_base,
ctt-term-meaning_wf,
context-set_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
ifthenelse_wf,
eq_atom_wf,
ctt-op-sort_wf,
term-opr_wf,
ctt-type-meaning_wf,
int_seg_wf,
ctt-level-type_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
eqtt_to_assert,
assert_of_eq_atom,
equal_wf,
eqff_to_assert,
bool_cases_sqequal,
assert-bnot,
neg_assert_of_eq_atom,
btrue_wf,
int_seg_subtype_nat,
istype-false,
bfalse_wf,
subtype_rel_universe1,
uiff_transitivity,
assert_of_bnot,
term-opr_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
isectEquality,
cumulativity,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
because_Cache,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
tokenEquality,
productEquality,
dependent_set_memberEquality_alt,
productElimination,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
voidElimination,
hyp_replacement,
applyLambdaEquality,
closedConclusion,
lambdaFormation_alt,
equalityElimination,
equalityIstype,
promote_hyp
Latex:
\mforall{}[ctxt:?CubicalContext]. \mforall{}[t,t':CttTerm]. [[ctxt;t]] = [[ctxt;t']] supposing ctt-eq\{i:l\}(t;t')
Date html generated:
2020_05_21-AM-10_33_44
Last ObjectModification:
2020_05_13-PM-04_36_16
Theory : cubical!type!theory
Home
Index