Nuprl Lemma : r-comp-r
∀[I:fset(ℕ)]. ∀[i:ℕ]. (r_i ⋅ r_i = 1 ∈ I+i ⟶ I+i)
Proof
Definitions occuring in Statement :
nc-r: r_i,
add-name: I+i,
nh-comp: g ⋅ f,
nh-id: 1,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
names-hom: I ⟶ J,
nh-id: 1,
top: Top,
compose: f o g,
nc-r: r_i,
names: names(I),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
DeMorgan-algebra: DeMorganAlgebra
Lemmas referenced :
names_wf,
add-name_wf,
nat_wf,
fset_wf,
nh-comp-sq,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
lattice-point_wf,
dM_wf,
nc-r_wf,
trivial-member-add-name1,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
dM_inc_wf,
nat_properties,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
intformand_wf,
int_formula_prop_and_lemma,
dM-lift-opp,
iff_weakening_equal,
dM-lift-inc,
int_subtype_base,
squash_wf,
true_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
dma-neg-dM_opp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
axiomEquality,
because_Cache,
voidElimination,
voidEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
applyEquality,
dependent_set_memberEquality,
intEquality,
lambdaEquality,
natural_numberEquality,
int_eqEquality,
computeAll,
independent_pairFormation,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality,
productEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. (r\_i \mcdot{} r\_i = 1)
Date html generated:
2017_10_05-AM-01_02_36
Last ObjectModification:
2017_07_28-AM-09_26_21
Theory : cubical!type!theory
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