Nuprl Lemma : ctt-op_wf
CttOp ∈ 𝕌'
Proof
Definitions occuring in Statement :
ctt-op: CttOp,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
ctt-op: CttOp,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
l_member_wf,
cons_wf,
nil_wf,
istype-atom,
eq_atom_wf,
ctt-tokens_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
productEquality,
setEquality,
closedConclusion,
atomEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
tokenEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
cumulativity,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
lambdaFormation_alt,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
universeEquality
Latex:
CttOp \mmember{} \mBbbU{}'
Date html generated:
2020_05_20-PM-08_16_45
Last ObjectModification:
2020_02_10-PM-01_04_34
Theory : cubical!type!theory
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