Nuprl Lemma : replace-vars_wf
∀[opr:Type]. ∀[t:term(opr)]. ∀[s:(varname() × term(opr)) List].  (replace-vars(s;t) ∈ term(opr))
Proof
Definitions occuring in Statement : 
replace-vars: replace-vars(s;t)
, 
term: term(opr)
, 
varname: varname()
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
product: x:A × B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
false: False
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
not: ¬A
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
prop: ℙ
, 
guard: {T}
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
sq_type: SQType(T)
, 
coterm-fun: coterm-fun(opr;T)
, 
replace-vars: replace-vars(s;t)
, 
has-value: (a)↓
, 
bound-term: bound-term(opr)
, 
mkterm: mkterm(opr;bts)
, 
sq_stable: SqStable(P)
, 
squash: ↓T
, 
pi2: snd(t)
Lemmas referenced : 
nat_properties, 
full-omega-unsat, 
intformand_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
intformless_wf, 
istype-int, 
int_formula_prop_and_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_less_lemma, 
int_formula_prop_wf, 
ge_wf, 
istype-less_than, 
int_seg_properties, 
int_seg_wf, 
subtract-1-ge-0, 
decidable__equal_int, 
subtract_wf, 
subtype_base_sq, 
set_subtype_base, 
int_subtype_base, 
intformnot_wf, 
intformeq_wf, 
itermSubtract_wf, 
int_formula_prop_not_lemma, 
int_formula_prop_eq_lemma, 
int_term_value_subtract_lemma, 
decidable__le, 
decidable__lt, 
istype-le, 
subtype_rel_self, 
term-ext, 
subtype_rel_weakening, 
term_wf, 
coterm-fun_wf, 
ext-eq_inversion, 
list_wf, 
varname_wf, 
term-size_wf, 
itermAdd_wf, 
int_term_value_add_lemma, 
istype-nat, 
istype-universe, 
apply-alist_wf, 
var-deq_wf, 
value-type-has-value, 
bound-term_wf, 
list-value-type, 
mkterm_wf, 
list-subtype, 
l_member_wf, 
eager-map_wf, 
product-value-type, 
term-size-positive, 
term_size_mkterm_lemma, 
summand-le-lsum, 
pi2_wf, 
sq_stable__le
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
cut, 
lambdaFormation_alt, 
thin, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
setElimination, 
rename, 
sqequalRule, 
intWeakElimination, 
natural_numberEquality, 
independent_isectElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
int_eqEquality, 
dependent_functionElimination, 
Error :memTop, 
independent_pairFormation, 
universeIsType, 
voidElimination, 
isect_memberEquality_alt, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isectIsTypeImplies, 
inhabitedIsType, 
functionIsTypeImplies, 
productElimination, 
unionElimination, 
applyEquality, 
instantiate, 
because_Cache, 
applyLambdaEquality, 
dependent_set_memberEquality_alt, 
productIsType, 
promote_hyp, 
hypothesis_subsumption, 
productEquality, 
equalityIstype, 
addEquality, 
universeEquality, 
callbyvalueReduce, 
independent_pairEquality, 
setIsType, 
setEquality, 
imageMemberEquality, 
baseClosed, 
imageElimination
Latex:
\mforall{}[opr:Type].  \mforall{}[t:term(opr)].  \mforall{}[s:(varname()  \mtimes{}  term(opr))  List].    (replace-vars(s;t)  \mmember{}  term(opr))
Date html generated:
2020_05_19-PM-09_57_31
Last ObjectModification:
2020_03_09-PM-04_09_48
Theory : terms
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