Nuprl Lemma : equiv-substs_wf
∀[opr:Type]. ∀[s1,s2:(varname() × term(opr)) List].  (equiv-substs(opr;s1;s2) ∈ ℙ)
Proof
Definitions occuring in Statement : 
equiv-substs: equiv-substs(opr;s1;s2)
, 
term: term(opr)
, 
varname: varname()
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
product: x:A × B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
equiv-substs: equiv-substs(opr;s1;s2)
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
isl: isl(x)
, 
outl: outl(x)
, 
uimplies: b supposing a
, 
not: ¬A
, 
false: False
Lemmas referenced : 
varname_wf, 
equal_wf, 
bool_wf, 
apply-alist_wf, 
var-deq_wf, 
term_wf, 
btrue_wf, 
bfalse_wf, 
assert_wf, 
alpha-eq-terms_wf, 
assert_elim, 
btrue_neq_bfalse, 
list_wf, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
functionEquality, 
extract_by_obid, 
hypothesis, 
productEquality, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
inhabitedIsType, 
lambdaFormation_alt, 
unionElimination, 
equalityIstype, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
because_Cache, 
independent_isectElimination, 
dependent_set_memberEquality_alt, 
independent_pairFormation, 
productIsType, 
applyLambdaEquality, 
setElimination, 
rename, 
productElimination, 
voidElimination, 
axiomEquality, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
universeIsType, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  \mforall{}[s1,s2:(varname()  \mtimes{}  term(opr))  List].    (equiv-substs(opr;s1;s2)  \mmember{}  \mBbbP{})
Date html generated:
2020_05_19-PM-09_57_35
Last ObjectModification:
2020_03_09-PM-04_09_52
Theory : terms
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