Nuprl Lemma : alpha-aux-trans
∀[opr:Type]
∀a,b,c:term(opr). ∀us,vs,ws:varname() List.
(alpha-aux(opr;us;vs;a;b) ⇒ alpha-aux(opr;vs;ws;b;c) ⇒ alpha-aux(opr;us;ws;a;c))
Proof
Definitions occuring in Statement :
alpha-aux: alpha-aux(opr;vs;ws;a;b),
term: term(opr),
varname: varname(),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
guard: {T},
pi2: snd(t),
bound-term: bound-term(opr),
mkterm: mkterm(opr;bts),
varterm: varterm(v),
alpha-aux: alpha-aux(opr;vs;ws;a;b),
false: False,
not: ¬A,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
pi1: fst(t)
Lemmas referenced :
istype-universe,
istype-void,
l_member_wf,
bound-term_wf,
mkterm_wf,
nullvar_wf,
varterm_wf,
alpha-aux_wf,
varname_wf,
list_wf,
term_wf,
term-induction,
same-binding-trans,
alpha-aux-mkterm,
istype-int,
length_wf_nat,
set_subtype_base,
le_wf,
int_subtype_base,
int_seg_wf,
length_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
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,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
rev-append_wf,
istype-le,
istype-less_than,
select_member
Rules used in proof :
universeEquality,
instantiate,
setIsType,
productElimination,
functionIsType,
equalityIstype,
equalitySymmetry,
equalityTransitivity,
inhabitedIsType,
voidElimination,
independent_isectElimination,
because_Cache,
rename,
setElimination,
lambdaFormation_alt,
independent_functionElimination,
universeIsType,
hypothesis,
functionEquality,
lambdaEquality_alt,
sqequalRule,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_functionElimination,
productIsType,
applyEquality,
intEquality,
natural_numberEquality,
sqequalBase,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
dependent_set_memberEquality_alt
Latex:
\mforall{}[opr:Type]
\mforall{}a,b,c:term(opr). \mforall{}us,vs,ws:varname() List.
(alpha-aux(opr;us;vs;a;b) {}\mRightarrow{} alpha-aux(opr;vs;ws;b;c) {}\mRightarrow{} alpha-aux(opr;us;ws;a;c))
Date html generated:
2020_05_19-PM-09_55_35
Last ObjectModification:
2020_03_12-PM-01_10_26
Theory : terms
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