Nuprl Lemma : subtype_rel_algebra
∀A1,A2:Type. ((A1 ⊆r A2) ⇒ (algebra_sig{i:l}(A2) ⊆r algebra_sig{[i | j]:l}(A1)))
Proof
Definitions occuring in Statement :
algebra_sig: algebra_sig{i:l}(A),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_product,
bool_wf,
unit_wf2,
subtype_rel_dep_function,
subtype_rel_self,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
universeEquality,
lambdaEquality,
productEquality,
functionEquality,
hypothesisEquality,
hypothesis,
unionEquality,
independent_isectElimination,
because_Cache
Latex:
\mforall{}A1,A2:Type. ((A1 \msubseteq{}r A2) {}\mRightarrow{} (algebra\_sig\{i:l\}(A2) \msubseteq{}r algebra\_sig\{[i | j]:l\}(A1)))
Date html generated:
2016_05_16-AM-07_26_14
Last ObjectModification:
2015_12_28-PM-05_08_35
Theory : algebras_1
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