Nuprl Lemma : ctt-opr-is-implies
∀[f:CttOp]. ∀[s:Atom]. f ~ <"opid", s> supposing ↑ctt-opr-is(f;s)
Proof
Definitions occuring in Statement :
ctt-opr-is: ctt-opr-is(f;s),
ctt-op: CttOp,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pair: <a, b>,
token: "$token",
atom: Atom,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
ctt-op: CttOp,
ctt-opr-is: ctt-opr-is(f;s),
subtype_rel: A ⊆r B,
not: ¬A,
false: False,
or: P ∨ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
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,
assert: ↑b,
prop: ℙ
Lemmas referenced :
subtype_base_sq,
product_subtype_base,
atom_subtype_base,
istype-assert,
ctt-opr-is_wf,
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,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
iff_imp_equal_bool,
bfalse_wf,
iff_functionality_wrt_iff,
false_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
productEquality,
atomEquality,
independent_isectElimination,
sqequalRule,
lambdaEquality_alt,
inhabitedIsType,
hypothesisEquality,
hypothesis,
lambdaFormation_alt,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomSqEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
productElimination,
setElimination,
rename,
tokenEquality,
because_Cache,
applyEquality,
baseClosed,
equalityIstype,
sqequalBase,
functionIsType,
unionElimination,
independent_pairFormation,
promote_hyp,
independent_pairEquality,
voidElimination
Latex:
\mforall{}[f:CttOp]. \mforall{}[s:Atom]. f \msim{} <"opid", s> supposing \muparrow{}ctt-opr-is(f;s)
Date html generated:
2020_05_20-PM-08_21_53
Last ObjectModification:
2020_03_17-AM-11_31_43
Theory : cubical!type!theory
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