Nuprl Lemma : sq_stable__alpha-aux
∀[opr:Type]. ∀a,b:term(opr). ∀vs,ws:varname() List. SqStable(alpha-aux(opr;vs;ws;a;b))
Proof
Definitions occuring in Statement :
alpha-aux: alpha-aux(opr;vs;ws;a;b),
term: term(opr),
varname: varname(),
list: T List,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
uimplies: b supposing a,
not: ¬A,
false: False,
alpha-aux: alpha-aux(opr;vs;ws;a;b),
varterm: varterm(v),
mkterm: mkterm(opr;bts),
bound-term: bound-term(opr),
pi2: snd(t),
guard: {T},
nil: [],
it: ⋅,
or: P ∨ Q,
cons: [a / b],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
sq_stable: SqStable(P),
subtype_rel: A ⊆r B,
nat: ℕ,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
le: A ≤ B,
less_than': less_than'(a;b),
select: L[n],
cand: A c∧ B,
nat_plus: ℕ+,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
uiff: uiff(P;Q),
ge: i ≥ j
Lemmas referenced :
term-induction,
term_wf,
list_wf,
varname_wf,
sq_stable_wf,
alpha-aux_wf,
all_wf,
varterm_wf,
sq_stable_from_decidable,
assert_wf,
same-binding_wf,
decidable__assert,
false_wf,
decidable__false,
bound-term_wf,
l_member_wf,
nullvar_wf,
istype-void,
mkterm_wf,
list_induction,
list-cases,
sq_stable__equal,
product_subtype_list,
nil_wf,
cons_member,
cons_wf,
spread_cons_lemma,
sq_stable__and,
equal-wf-base,
length_wf_nat,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
rev-append_wf,
istype-universe,
istype-le,
length_of_cons_lemma,
add_nat_plus,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
nat_plus_properties,
add-is-int-iff,
intformand_wf,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
length_wf,
select_wf,
nat_properties,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
functionEquality,
hypothesis,
universeIsType,
independent_functionElimination,
lambdaFormation_alt,
because_Cache,
setElimination,
rename,
independent_isectElimination,
voidElimination,
inhabitedIsType,
dependent_functionElimination,
functionIsType,
equalityIstype,
productElimination,
setIsType,
unionElimination,
promote_hyp,
hypothesis_subsumption,
inrFormation_alt,
productEquality,
independent_pairEquality,
Error :memTop,
functionIsTypeImplies,
spreadEquality,
intEquality,
applyEquality,
natural_numberEquality,
isect_memberEquality_alt,
productIsType,
sqequalBase,
equalitySymmetry,
instantiate,
universeEquality,
dependent_pairFormation_alt,
dependent_set_memberEquality_alt,
independent_pairFormation,
approximateComputation,
equalityTransitivity,
applyLambdaEquality,
pointwiseFunctionality,
baseApply,
closedConclusion,
baseClosed,
int_eqEquality
Latex:
\mforall{}[opr:Type]. \mforall{}a,b:term(opr). \mforall{}vs,ws:varname() List. SqStable(alpha-aux(opr;vs;ws;a;b))
Date html generated:
2020_05_19-PM-09_55_25
Last ObjectModification:
2020_03_09-PM-04_08_53
Theory : terms
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