Nuprl Lemma : eq_var_wf
∀[a,b:varname()]. (eq_var(a;b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
eq_var: eq_var(a;b),
varname: varname(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
varname: varname(),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
eq_var: eq_var(a;b),
pi2: snd(t),
all: ∀x:A. B[x],
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
nat: ℕ,
bfalse: ff,
band: p ∧b q
Lemmas referenced :
eq_atom_wf,
bfalse_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
band_wf,
btrue_wf,
assert_of_eq_atom,
eq_int_wf,
varname_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
isatomReduceTrue,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
because_Cache,
dependent_functionElimination,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
setElimination,
rename,
inhabitedIsType,
universeIsType
Latex:
\mforall{}[a,b:varname()]. (eq\_var(a;b) \mmember{} \mBbbB{})
Date html generated:
2020_05_19-PM-09_52_59
Last ObjectModification:
2020_03_09-PM-04_07_56
Theory : terms
Home
Index