Nuprl Lemma : ctt-is-fibrant_wf
∀[t:term(CttOp)]. (ctt-is-fibrant(t) ∈ 𝔹)
Proof
Definitions occuring in Statement :
ctt-is-fibrant: ctt-is-fibrant(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-fibrant: ctt-is-fibrant(t),
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,
exists: ∃x:A. B[x],
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
bfalse: ff,
false: False,
subtype_rel: A ⊆r B,
band: p ∧b q
Lemmas referenced :
bnot_wf,
isvarterm_wf,
ctt-op_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
band_wf,
btrue_wf,
bool_cases_sqequal,
eqff_to_assert,
assert-bnot,
eq_atom_wf,
ctt-op-sort_wf,
term-opr_wf,
bfalse_wf,
term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
unionElimination,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productElimination,
dependent_pairFormation_alt,
equalityIstype,
inhabitedIsType,
promote_hyp,
because_Cache,
voidElimination,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
tokenEquality,
axiomEquality,
universeIsType
Latex:
\mforall{}[t:term(CttOp)]. (ctt-is-fibrant(t) \mmember{} \mBbbB{})
Date html generated:
2020_05_21-AM-10_35_58
Last ObjectModification:
2020_02_12-PM-04_08_07
Theory : cubical!type!theory
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