Nuprl Lemma : alpha-equal-varterm
∀[opr:Type]. ∀[v:{v:varname()| ¬(v = nullvar() ∈ varname())} ]. ∀[t:term(opr)].
  t = varterm(v) ∈ term(opr) supposing alpha-eq-terms(opr;varterm(v);t)
Proof
Definitions occuring in Statement : 
alpha-eq-terms: alpha-eq-terms(opr;a;b)
, 
varterm: varterm(v)
, 
term: term(opr)
, 
nullvar: nullvar()
, 
varname: varname()
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
set: {x:A| B[x]} 
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
isvarterm: isvarterm(t)
, 
isl: isl(x)
, 
varterm: varterm(v)
, 
btrue: tt
, 
all: ∀x:A. B[x]
, 
or: P ∨ Q
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
prop: ℙ
, 
squash: ↓T
, 
true: True
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
alpha-eq-terms: alpha-eq-terms(opr;a;b)
, 
alpha-aux: alpha-aux(opr;vs;ws;a;b)
, 
same-binding: same-binding(vs;ws;v;w)
, 
nil: []
, 
it: ⋅
, 
uiff: uiff(P;Q)
, 
mkterm: mkterm(opr;bts)
, 
bfalse: ff
Lemmas referenced : 
isvarterm_functionality, 
varterm_wf, 
btrue_wf, 
term-cases, 
alpha-eq-terms_wf, 
nullvar_wf, 
term_wf, 
varname_wf, 
istype-void, 
istype-universe, 
subtype_rel_self, 
iff_weakening_equal, 
assert-eq_var, 
equal_wf, 
squash_wf, 
true_wf, 
not_wf, 
equal-wf-T-base, 
btrue_neq_bfalse, 
bool_wf, 
bfalse_wf, 
isvarterm_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
because_Cache, 
independent_isectElimination, 
setElimination, 
rename, 
lambdaFormation_alt, 
hypothesis, 
independent_functionElimination, 
voidElimination, 
equalitySymmetry, 
sqequalRule, 
equalityTransitivity, 
dependent_functionElimination, 
unionElimination, 
productElimination, 
universeIsType, 
equalityIstype, 
inhabitedIsType, 
isect_memberEquality_alt, 
axiomEquality, 
isectIsTypeImplies, 
setIsType, 
functionIsType, 
instantiate, 
universeEquality, 
applyEquality, 
lambdaEquality_alt, 
imageElimination, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
hyp_replacement, 
dependent_set_memberEquality_alt, 
independent_pairFormation, 
productIsType, 
applyLambdaEquality
Latex:
\mforall{}[opr:Type].  \mforall{}[v:\{v:varname()|  \mneg{}(v  =  nullvar())\}  ].  \mforall{}[t:term(opr)].
    t  =  varterm(v)  supposing  alpha-eq-terms(opr;varterm(v);t)
Date html generated:
2020_05_19-PM-09_55_53
Last ObjectModification:
2020_05_13-PM-04_48_24
Theory : terms
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