Nuprl Lemma : sub-co-list_transitivity
∀[T:Type]. ∀[s1,s2,s3:colist(T)]. (sub-co-list(T;s1;s2) ⇒ sub-co-list(T;s2;s3) ⇒ sub-co-list(T;s1;s3))
Proof
Definitions occuring in Statement :
sub-co-list: sub-co-list(T;s1;s2),
colist: colist(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
sub-co-list: sub-co-list(T;s1;s2),
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
false: False,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
sub-co-list_wf,
colist_wf,
istype-universe,
combine-skips_wf,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
list-at_wf,
equal_wf,
squash_wf,
true_wf,
list-at-at,
subtype_rel_self,
iff_weakening_equal,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
instantiate,
universeEquality,
Error :dependent_pairFormation_alt,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[s1,s2,s3:colist(T)].
(sub-co-list(T;s1;s2) {}\mRightarrow{} sub-co-list(T;s2;s3) {}\mRightarrow{} sub-co-list(T;s1;s3))
Date html generated:
2019_06_20-PM-01_21_59
Last ObjectModification:
2018_12_07-PM-06_34_14
Theory : list_1
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