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
Home
Index