Nuprl Lemma : test-mutual-corec_wf
test-mutual-corec() ∈ ℕ2 ⟶ Type
Proof
Definitions occuring in Statement :
test-mutual-corec: test-mutual-corec(),
int_seg: {i..j-},
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
test-mutual-corec: test-mutual-corec(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
mutual-corec_wf,
false_wf,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
unit_wf2,
int_seg_wf,
lelt_wf,
list_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
lambdaEquality,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
unionEquality,
productEquality,
applyEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
functionEquality,
universeEquality
Latex:
test-mutual-corec() \mmember{} \mBbbN{}2 {}\mrightarrow{} Type
Date html generated:
2018_05_21-PM-00_31_19
Last ObjectModification:
2017_10_18-PM-06_38_23
Theory : int_2
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