Nuprl Lemma : isvarterm_functionality
∀[opr:Type]. ∀[t,t':term(opr)].  isvarterm(t) = isvarterm(t') supposing alpha-eq-terms(opr;t;t')
Proof
Definitions occuring in Statement : 
alpha-eq-terms: alpha-eq-terms(opr;a;b)
, 
isvarterm: isvarterm(t)
, 
term: term(opr)
, 
bool: 𝔹
, 
uimplies: b supposing a
, 
uall: ∀[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
, 
all: ∀x:A. B[x]
, 
or: P ∨ Q
, 
prop: ℙ
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
sq_type: SQType(T)
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
true: True
, 
isvarterm: isvarterm(t)
, 
isl: isl(x)
, 
varterm: varterm(v)
, 
btrue: tt
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
false: False
, 
alpha-eq-terms: alpha-eq-terms(opr;a;b)
, 
alpha-aux: alpha-aux(opr;vs;ws;a;b)
, 
mkterm: mkterm(opr;bts)
, 
bfalse: ff
Lemmas referenced : 
term-cases, 
alpha-eq-terms_wf, 
subtype_base_sq, 
bool_wf, 
bool_subtype_base, 
btrue_wf, 
equal_wf, 
squash_wf, 
true_wf, 
istype-universe, 
isvarterm_wf, 
term_wf, 
subtype_rel_self, 
iff_weakening_equal, 
bfalse_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_functionElimination, 
unionElimination, 
hypothesis, 
universeIsType, 
sqequalRule, 
isect_memberEquality_alt, 
axiomEquality, 
isectIsTypeImplies, 
inhabitedIsType, 
because_Cache, 
productElimination, 
instantiate, 
cumulativity, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
natural_numberEquality, 
applyEquality, 
lambdaEquality_alt, 
imageElimination, 
universeEquality, 
imageMemberEquality, 
baseClosed, 
voidElimination, 
hyp_replacement
Latex:
\mforall{}[opr:Type].  \mforall{}[t,t':term(opr)].    isvarterm(t)  =  isvarterm(t')  supposing  alpha-eq-terms(opr;t;t')
Date html generated:
2020_05_19-PM-09_55_51
Last ObjectModification:
2020_05_13-PM-03_40_27
Theory : terms
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