Nuprl Lemma : subtype_rel_FOAssignment
∀[vs1,vs2:ℤ List]. ∀[Dom:Type]. FOAssignment(vs1,Dom) ⊆r FOAssignment(vs2,Dom) supposing vs2 ⊆ vs1
Proof
Definitions occuring in Statement :
FOAssignment: FOAssignment(vs,Dom),
l_contains: A ⊆ B,
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
FOAssignment: FOAssignment(vs,Dom),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
l_contains_wf,
list_wf,
l_member_wf,
l_contains-member,
set_wf,
subtype_rel_dep_function,
subtype_rel_sets
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
setEquality,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
independent_isectElimination,
setElimination,
rename,
lambdaFormation
Latex:
\mforall{}[vs1,vs2:\mBbbZ{} List]. \mforall{}[Dom:Type]. FOAssignment(vs1,Dom) \msubseteq{}r FOAssignment(vs2,Dom) supposing vs2 \msubseteq{} vs1
Date html generated:
2016_05_15-PM-10_11_56
Last ObjectModification:
2015_12_27-PM-06_33_57
Theory : minimal-first-order-logic
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