Nuprl Lemma : cnv-taba_wf
∀[A,B:Type]. ∀xs:A List. ∀ys:B List. ((||xs|| ≤ ||ys||) ⇒ (cnv-taba(xs;ys) ∈ (A × B) List))
Proof
Definitions occuring in Statement :
cnv-taba: cnv-taba(xs;ys),
length: ||as||,
list: T List,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
cnv-taba: cnv-taba(xs;ys),
nat: ℕ,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
or: P ∨ Q,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
pi2: snd(t),
le: A ≤ B,
uiff: uiff(P;Q)
Lemmas referenced :
le_wf,
length_wf,
list_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
length_of_nil_lemma,
list_ind_nil_lemma,
product_subtype_list,
spread_cons_lemma,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
equal_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
length_of_cons_lemma,
list_ind_cons_lemma,
nil_wf,
pi2_wf,
add-is-int-iff,
false_wf,
set_wf,
spread_wf,
cons_wf,
pi1_wf_top,
subtype_rel_product,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
universeEquality,
isect_memberEquality,
isectElimination,
extract_by_obid,
cumulativity,
lambdaFormation,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
applyEquality,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
baseClosed,
instantiate,
imageElimination,
independent_pairEquality,
productEquality,
pointwiseFunctionality,
baseApply,
closedConclusion
Latex:
\mforall{}[A,B:Type]. \mforall{}xs:A List. \mforall{}ys:B List. ((||xs|| \mleq{} ||ys||) {}\mRightarrow{} (cnv-taba(xs;ys) \mmember{} (A \mtimes{} B) List))
Date html generated:
2018_05_21-PM-09_00_04
Last ObjectModification:
2017_07_26-PM-06_23_30
Theory : general
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