Nuprl Lemma : algebra_sig_inc
∀A:Type. (algebra_sig{i:l}(A) ⊆r algebra_sig{[i | j]:l}(A))
Proof
Definitions occuring in Statement :
algebra_sig: algebra_sig{i:l}(A),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_algebra
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
independent_functionElimination,
lambdaEquality,
hypothesis,
universeEquality
Latex:
\mforall{}A:Type. (algebra\_sig\{i:l\}(A) \msubseteq{}r algebra\_sig\{[i | j]:l\}(A))
Date html generated:
2019_10_16-PM-00_58_32
Last ObjectModification:
2018_09_17-PM-06_21_13
Theory : algebras_1
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