Nuprl Lemma : ctt-binder-context_wf
ctt-binder-context ∈ ?CubicalContext
⟶ (varname() List)
⟶ CttOp
⟶ very-dep-fun(?CubicalContext;varname() List × CttTerm;a,bt.[[a;snd(bt)]])
Proof
Definitions occuring in Statement :
ctt-binder-context: ctt-binder-context,
ctt_meaning: [[ctxt;t]],
ctt-term: CttTerm,
ctt-op: CttOp,
cubical-context: ?CubicalContext,
varname: varname(),
very-dep-fun: very-dep-fun(A;B;a,b.C[a; b]),
list: T List,
pi2: snd(t),
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
ctt-binder-context: ctt-binder-context,
member: t ∈ T,
select: L[n],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
pi1: fst(t),
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
nat: ℕ,
cand: A c∧ B,
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
sq_type: SQType(T),
guard: {T},
true: True,
subtype_rel: A ⊆r B,
pi2: snd(t),
or: P ∨ Q,
decidable: Dec(P),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
very-dep-fun: very-dep-fun(A;B;a,b.C[a; b]),
ge: i ≥ j ,
vdf: vdf(A;B;a,b.C[a; b];n),
lt_int: i <z j,
subtract: n - m,
cons: [a / b],
less_than: a < b,
squash: ↓T,
ctt-term: CttTerm,
wfterm: wfterm(opr;sort;arity),
provisional-subterm-context: provisional-subterm-context{i:l}(X;f;vs;L),
eq_int: (i =z j),
bor: p ∨bq,
ctt-subterm-context: ctt-subterm-context{i:l}(ctxt;f;n;vs;m),
ctt-opr-is: ctt-opr-is(f;s),
eq_atom: x =a y,
int_iseg: {i...j},
bdd-all: bdd-all(n;i.P[i])
Lemmas referenced :
length_of_nil_lemma,
stuck-spread,
istype-base,
bdd_all_zero_lemma,
length_wf,
nat_wf,
ctt-arity_wf,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
varname_wf,
select_wf,
istype-false,
eq_int_wf,
assert_of_eq_int,
provisional-subterm-context_wf,
nil_wf,
cubical-context_wf,
list_wf,
ctt-term_wf,
ctt_meaning_wf,
pi2_wf,
int_seg_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
subtype_base_sq,
int_subtype_base,
istype-less_than,
length_wf_nat,
pi1_wf_top,
set_subtype_base,
le_wf,
ctt-kind_wf,
istype-assert,
ctt-opr-is_wf,
decidable__lt,
intformnot_wf,
intformeq_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
iff_weakening_uiff,
assert_wf,
less_than_wf,
decidable__le,
istype-le,
nat_properties,
ge_wf,
list-cases,
product_subtype_list,
le_weakening2,
length_of_cons_lemma,
non_neg_length,
itermAdd_wf,
int_term_value_add_lemma,
equal-wf-base,
subtract-1-ge-0,
vdf-eq-implies,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtract-add-cancel,
bdd-all_wf,
bind-provision-cubical-context-equations,
assert-bdd-all,
equal_wf,
subtype_rel_self,
iff_weakening_equal,
subtype_rel_product,
top_wf,
vdf-eq_wf1,
ctt-op_wf,
subtype_rel_list,
band_tt,
equal-wf-T-base,
band_ff,
bor_wf,
ctt-opr-is-implies,
bnot_wf,
not_wf,
istype-void,
primrec1_lemma,
firstn_wf,
length_firstn_eq,
select-firstn,
bool_cases,
band_wf,
btrue_wf,
bfalse_wf,
first0,
uiff_transitivity,
iff_transitivity,
assert_of_bnot,
length_firstn,
assert_of_band,
bnot_thru_band,
assert_of_bor
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
functionExtensionality,
sqequalRule,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
lambdaFormation_alt,
Error :memTop,
dependent_functionElimination,
closedConclusion,
natural_numberEquality,
productEquality,
hypothesisEquality,
because_Cache,
inhabitedIsType,
unionElimination,
equalityElimination,
productElimination,
lambdaEquality_alt,
independent_pairFormation,
setElimination,
rename,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_set_memberEquality_alt,
instantiate,
cumulativity,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
universeIsType,
voidElimination,
intEquality,
sqequalBase,
productIsType,
applyEquality,
functionIsType,
unionIsType,
tokenEquality,
promote_hyp,
isect_memberEquality_alt,
intWeakElimination,
axiomEquality,
functionIsTypeImplies,
hypothesis_subsumption,
setEquality,
dependentIntersection_memberEquality,
independent_pairEquality,
imageElimination,
imageMemberEquality,
universeEquality,
unionEquality,
inlFormation_alt,
inrFormation_alt
Latex:
ctt-binder-context \mmember{} ?CubicalContext
{}\mrightarrow{} (varname() List)
{}\mrightarrow{} CttOp
{}\mrightarrow{} very-dep-fun(?CubicalContext;varname() List \mtimes{} CttTerm;a,bt.[[a;snd(bt)]])
Date html generated:
2020_05_21-AM-10_38_24
Last ObjectModification:
2020_05_18-AM-11_26_18
Theory : cubical!type!theory
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