Nuprl Lemma : ctt-is-term_wf
∀[t:term(CttOp)]. (ctt-is-term(t) ∈ 𝔹)
Proof
Definitions occuring in Statement :
ctt-is-term: ctt-is-term(t),
ctt-op: CttOp,
term: term(opr),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-is-term: ctt-is-term(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B
Lemmas referenced :
isvarterm_wf,
ctt-op_wf,
eqtt_to_assert,
btrue_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
eq_atom_wf,
ctt-op-sort_wf,
term-opr_wf,
term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
hypothesisEquality,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
dependent_functionElimination,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
tokenEquality,
universeIsType
Latex:
\mforall{}[t:term(CttOp)]. (ctt-is-term(t) \mmember{} \mBbbB{})
Date html generated:
2020_05_21-AM-10_34_51
Last ObjectModification:
2020_02_12-AM-11_21_03
Theory : cubical!type!theory
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