Nuprl Lemma : name-morph-1-satisfies
∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. (1 f) = 1
Proof
Definitions occuring in Statement :
name-morph-satisfies: (psi f) = 1,
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
lattice-1: 1,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-satisfies: (psi f) = 1,
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 :
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,
fl-morph-1,
lattice-1_wf,
bdd-distributive-lattice_wf,
iff_weakening_equal,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
sqequalRule,
instantiate,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
setElimination,
rename,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. (1 f) = 1
Date html generated:
2017_10_05-AM-01_18_10
Last ObjectModification:
2017_07_28-AM-09_33_26
Theory : cubical!type!theory
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