Nuprl Lemma : int_formulaco_wf
int_formulaco() ∈ Type
Proof
Definitions occuring in Statement :
int_formulaco: int_formulaco(),
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
int_formulaco: int_formulaco(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s]
Lemmas referenced :
corec_wf,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
int_term_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
productEquality,
atomEquality,
hypothesisEquality,
tokenEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
voidEquality,
universeEquality
Latex:
int\_formulaco() \mmember{} Type
Date html generated:
2017_04_14-AM-08_59_42
Last ObjectModification:
2017_02_27-PM-03_41_51
Theory : omega
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