Nuprl Lemma : nh-id-left
∀I,J:fset(ℕ). ∀f:I ⟶ J. (f ⋅ 1 = f ∈ I ⟶ J)
Proof
Definitions occuring in Statement :
nh-comp: g ⋅ f,
nh-id: 1,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
nh-id: 1,
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
dM_inc: <x>,
dma-lift-compose: dma-lift-compose(I;J;eqi;eqj;f;g),
member: t ∈ T,
uall: ∀[x:A]. B[x],
compose: f o g,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
dma-hom: dma-hom(dma1;dma2),
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
dM: dM(I),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
free-dma-lift-id,
names_wf,
names-deq_wf,
equal_wf,
squash_wf,
true_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
dma-hom_wf,
free-DeMorgan-algebra_wf,
iff_weakening_equal,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
functionExtensionality,
sqequalHypSubstitution,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
instantiate,
productEquality,
independent_isectElimination,
cumulativity,
because_Cache,
setElimination,
rename,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}I,J:fset(\mBbbN{}). \mforall{}f:I {}\mrightarrow{} J. (f \mcdot{} 1 = f)
Date html generated:
2017_10_05-AM-01_01_45
Last ObjectModification:
2017_07_28-AM-09_25_57
Theory : cubical!type!theory
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