Nuprl Lemma : set_subtype_base

`∀[A:Type]. ∀[P:A ⟶ ℙ].  {a:A| P[a]}  ⊆r Base supposing A ⊆r Base`

Proof

Definitions occuring in Statement :  uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` set: `{x:A| B[x]} ` function: `x:A ⟶ B[x]` base: `Base` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` guard: `{T}` subtype_rel: `A ⊆r B` so_apply: `x[s]` prop: `ℙ`
Lemmas referenced :  subtype_rel_transitivity base_wf subtype_rel_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution lambdaEquality setElimination thin rename hypothesisEquality setEquality applyEquality hypothesis sqequalRule universeEquality lemma_by_obid isectElimination because_Cache independent_isectElimination axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry functionEquality cumulativity

Latex:
\mforall{}[A:Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbP{}].    \{a:A|  P[a]\}    \msubseteq{}r  Base  supposing  A  \msubseteq{}r  Base

Date html generated: 2016_05_13-PM-03_19_28
Last ObjectModification: 2015_12_26-AM-09_07_38

Theory : subtype_0

Home Index