Nuprl Lemma : alpha-avoid-equivalent
∀[opr:Type]. ∀t:term(opr). ∀L:varname() List. alpha-eq-terms(opr;alpha-avoid(L;t);t) supposing ¬(nullvar() ∈ L)
Proof
Definitions occuring in Statement :
alpha-avoid: alpha-avoid(L;t),
alpha-eq-terms: alpha-eq-terms(opr;a;b),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
alpha-avoid: alpha-avoid(L;t),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
istype: istype(T),
and: P ∧ Q,
cand: A c∧ B,
alist-map: alist-map(eq;L),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
inject: Inj(A;B;f),
squash: ↓T,
label: ...$L... t,
true: True
Lemmas referenced :
alpha-rename-equivalent,
alist-map_wf,
varname_wf,
var-deq_wf,
alpha-rename-alist_wf,
subtype_rel_dep_function,
l_member_wf,
all-vars_wf,
free-vars_wf,
subtype_rel_list,
not_wf,
equal-wf-T-base,
nullvar_wf,
istype-void,
list_wf,
term_wf,
istype-universe,
apply-alist_wf,
alpha-rename-alist-property,
append_wf,
apply-alist-inl,
free-vars-all-vars,
member_append,
alpha-rename-alist-nonnullvar,
equal_wf,
squash_wf,
true_wf,
member_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality_alt,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
functionIsTypeImplies,
inhabitedIsType,
rename,
extract_by_obid,
isectElimination,
hypothesis,
applyEquality,
universeIsType,
setEquality,
setIsType,
independent_isectElimination,
setElimination,
because_Cache,
baseClosed,
functionIsType,
equalityIstype,
independent_pairFormation,
productElimination,
instantiate,
universeEquality,
unionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
inrFormation_alt,
imageElimination,
hyp_replacement,
applyLambdaEquality,
imageMemberEquality,
dependent_set_memberEquality_alt,
natural_numberEquality
Latex:
\mforall{}[opr:Type]
\mforall{}t:term(opr). \mforall{}L:varname() List.
alpha-eq-terms(opr;alpha-avoid(L;t);t) supposing \mneg{}(nullvar() \mmember{} L)
Date html generated:
2020_05_19-PM-09_57_27
Last ObjectModification:
2020_03_09-PM-04_09_45
Theory : terms
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