Nuprl Lemma : assert-ctt-opr-is
∀[f:CttOp]. ∀[s:Atom]. uiff(↑ctt-opr-is(f;s);f = <"opid", s> ∈ CttOp)
Proof
Definitions occuring in Statement :
ctt-opr-is: ctt-opr-is(f;s),
ctt-op: CttOp,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
pair: <a, b>,
token: "$token",
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
ctt-op: CttOp,
ctt-opr-is: ctt-opr-is(f;s),
so_lambda: λ2x.t[x],
so_apply: x[s],
not: ¬A,
false: False,
all: ∀x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
eq_atom: x =a y,
band: p ∧b q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
select: L[n],
cons: [a / b],
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
true: True,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
bnot: ¬bb,
assert: ↑b,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
istype-assert,
ctt-opr-is_wf,
assert_witness,
atom_subtype_base,
istype-atom,
ctt-op_wf,
eq_atom_wf,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
set_subtype_base,
l_member_wf,
cons_wf,
nil_wf,
istype-void,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
istype-le,
length_of_cons_lemma,
length_of_nil_lemma,
istype-less_than,
length_wf,
list_subtype_base,
le_wf,
istype-int,
int_subtype_base,
ctt-tokens_wf,
bool_cases_sqequal,
assert-bnot,
neg_assert_of_eq_atom,
nat_wf,
iff_imp_equal_bool,
bfalse_wf,
iff_functionality_wrt_iff,
false_wf,
iff_weakening_equal,
assert_functionality_wrt_uiff,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
independent_functionElimination,
equalityIstype,
inhabitedIsType,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
sqequalBase,
equalitySymmetry,
productElimination,
independent_pairEquality,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
universeIsType,
setElimination,
rename,
tokenEquality,
equalityTransitivity,
atomEquality,
lambdaEquality_alt,
independent_isectElimination,
functionIsType,
dependent_functionElimination,
unionElimination,
instantiate,
cumulativity,
lambdaFormation_alt,
promote_hyp,
dependent_pairEquality_alt,
dependent_pairFormation_alt,
dependent_set_memberEquality_alt,
natural_numberEquality,
voidElimination,
Error :memTop,
imageMemberEquality,
productIsType,
intEquality,
hyp_replacement,
applyLambdaEquality,
equalityElimination,
setEquality,
universeEquality,
productEquality,
imageElimination
Latex:
\mforall{}[f:CttOp]. \mforall{}[s:Atom]. uiff(\muparrow{}ctt-opr-is(f;s);f = <"opid", s>)
Date html generated:
2020_05_20-PM-08_21_33
Last ObjectModification:
2020_03_02-PM-04_11_20
Theory : cubical!type!theory
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