Nuprl Lemma : ctt-opr-is_wf
∀[f:CttOp]. ∀[s:Atom]. (ctt-opr-is(f;s) ∈ 𝔹)
Proof
Definitions occuring in Statement :
ctt-opr-is: ctt-opr-is(f;s),
ctt-op: CttOp,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-opr-is: ctt-opr-is(f;s),
ctt-op: CttOp,
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,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b,
false: False,
band: p ∧b q
Lemmas referenced :
eq_atom_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
band_wf,
btrue_wf,
assert_of_eq_atom,
l_member_wf,
ctt-tokens_wf,
eqff_to_assert,
bool_cases_sqequal,
bfalse_wf,
istype-atom,
ctt-op_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
closedConclusion,
tokenEquality,
dependent_functionElimination,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
applyEquality,
because_Cache,
inhabitedIsType,
lambdaFormation_alt,
equalityElimination,
lambdaEquality_alt,
setIsType,
universeIsType,
atomEquality,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
voidElimination,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[f:CttOp]. \mforall{}[s:Atom]. (ctt-opr-is(f;s) \mmember{} \mBbbB{})
Date html generated:
2020_05_20-PM-08_21_10
Last ObjectModification:
2020_02_15-AM-10_59_40
Theory : cubical!type!theory
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