Nuprl Lemma : irr-face-morph-satisfies
∀[I:fset(ℕ)]. ∀[as,bs:fset(names(I))].
(irr_face(I;as;bs) irr-face-morph(I;as;bs)) = 1 supposing ↑fset-disjoint(NamesDeq;as;bs)
Proof
Definitions occuring in Statement :
name-morph-satisfies: (psi f) = 1,
irr-face-morph: irr-face-morph(I;as;bs),
irr_face: irr_face(I;as;bs),
names-deq: NamesDeq,
names: names(I),
fset-disjoint: fset-disjoint(eq;as;bs),
fset: fset(T),
nat: ℕ,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
name-morph-satisfies: (psi f) = 1,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
irr-face-morph: irr-face-morph(I;as;bs),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
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,
not: ¬A
Lemmas referenced :
assert_wf,
fset-disjoint_wf,
names_wf,
names-deq_wf,
fset_wf,
nat_wf,
irr-face-morph_wf,
deq-fset-member_wf,
bool_wf,
eqtt_to_assert,
assert-deq-fset-member,
dM0_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
fset-member_wf,
dM1_wf,
satisfies-irr-face,
assert-fset-disjoint
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
hypothesis,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
independent_pairFormation
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[as,bs:fset(names(I))].
(irr\_face(I;as;bs) irr-face-morph(I;as;bs)) = 1 supposing \muparrow{}fset-disjoint(NamesDeq;as;bs)
Date html generated:
2018_05_23-AM-08_39_18
Last ObjectModification:
2017_11_09-AM-11_57_27
Theory : cubical!type!theory
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