### 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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