Nuprl Lemma : nh-comp_wf
∀[I,J,K:fset(ℕ)]. ∀[f:I ⟶ J]. ∀[g:J ⟶ K]. (g ⋅ f ∈ I ⟶ K)
Proof
Definitions occuring in Statement :
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
names-hom: I ⟶ J,
nh-comp: g ⋅ f,
dM: dM(I),
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
dma-lift-compose_wf,
names_wf,
names-deq_wf,
lattice-point_wf,
free-DeMorgan-algebra_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,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
sqequalRule,
applyEquality,
lambdaEquality,
functionEquality,
instantiate,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I,J,K:fset(\mBbbN{})]. \mforall{}[f:I {}\mrightarrow{} J]. \mforall{}[g:J {}\mrightarrow{} K]. (g \mcdot{} f \mmember{} I {}\mrightarrow{} K)
Date html generated:
2016_05_18-AM-11_59_32
Last ObjectModification:
2015_12_28-PM-03_07_19
Theory : cubical!type!theory
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