Nuprl Lemma : face-fl-morph-id
∀[I:fset(ℕ)]. ∀[phi:𝔽(I)]. ((phi)<1> = phi ∈ 𝔽(I))
Proof
Definitions occuring in Statement :
face-presheaf: 𝔽,
fl-morph: <f>,
I_cube: A(I),
nh-id: 1,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
face-presheaf: 𝔽,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
I_cube_pair_redex_lemma,
equal_wf,
squash_wf,
true_wf,
lattice-point_wf,
face_lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
apply-fl-morph-id,
iff_weakening_equal,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
instantiate,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[phi:\mBbbF{}(I)]. ((phi)ə> = phi)
Date html generated:
2017_10_05-AM-01_15_13
Last ObjectModification:
2017_07_28-AM-09_31_52
Theory : cubical!type!theory
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