Nuprl Lemma : alpha-rename-alist-nonnullvar
∀[opr:Type]
∀t:term(opr). ∀L:varname() List. ∀x,x':varname().
((<x, x'> ∈ alpha-rename-alist(t;L)) ⇒ (x' = nullvar() ∈ varname()) ⇒ (nullvar() ∈ L))
Proof
Definitions occuring in Statement :
alpha-rename-alist: alpha-rename-alist(t;L),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
pair: <a, b>,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
alpha-rename-alist: alpha-rename-alist(t;L),
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
has-value: (a)↓,
uimplies: b supposing a,
varname: varname(),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_apply: x[s1;s2],
guard: {T},
prop: ℙ,
implies: P ⇒ Q,
pi2: snd(t),
and: P ∧ Q,
nil: [],
it: ⋅,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
or: P ∨ Q,
pi1: fst(t),
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q
Lemmas referenced :
list_accum_invariant2,
varname_wf,
list_wf,
value-type-has-value,
bunion-value-type,
nat_wf,
atom-value-type,
product-value-type,
istype-atom,
maybe_new_var_wf,
cons_wf,
l_member_wf,
pi2_wf,
equal-wf-T-base,
nullvar_wf,
append_wf,
all-vars_wf,
nil_wf,
null_nil_lemma,
btrue_wf,
null_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
cons_member,
pi1_wf,
term_wf,
istype-universe,
maybe_new_var-is-null,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality_alt,
productElimination,
callbyvalueReduce,
independent_isectElimination,
atomEquality,
because_Cache,
hypothesisEquality,
independent_pairEquality,
closedConclusion,
universeIsType,
productIsType,
functionEquality,
inhabitedIsType,
baseClosed,
independent_functionElimination,
voidEquality,
equalitySymmetry,
dependent_set_memberEquality_alt,
independent_pairFormation,
equalityTransitivity,
equalityIstype,
applyLambdaEquality,
setElimination,
rename,
voidElimination,
unionElimination,
functionIsType,
instantiate,
universeEquality,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality
Latex:
\mforall{}[opr:Type]
\mforall{}t:term(opr). \mforall{}L:varname() List. \mforall{}x,x':varname().
((<x, x'> \mmember{} alpha-rename-alist(t;L)) {}\mRightarrow{} (x' = nullvar()) {}\mRightarrow{} (nullvar() \mmember{} L))
Date html generated:
2020_05_19-PM-09_57_15
Last ObjectModification:
2020_03_09-PM-04_09_37
Theory : terms
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