Nuprl Lemma : int_seg_subtype_upper

`∀[m1,n1,m2:ℤ].  {m1..n1-} ⊆r {m2...} supposing m2 ≤ m1`

Proof

Definitions occuring in Statement :  int_upper: `{i...}` int_seg: `{i..j-}` uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]` le: `A ≤ B` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` int_seg: `{i..j-}` int_upper: `{i...}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` lelt: `i ≤ j < k` and: `P ∧ Q` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` le: `A ≤ B` guard: `{T}`
Lemmas referenced :  subtype_rel_sets lelt_wf le_wf le_transitivity
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin intEquality because_Cache lambdaEquality hypothesisEquality hypothesis independent_isectElimination setElimination rename setEquality lambdaFormation productElimination axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[m1,n1,m2:\mBbbZ{}].    \{m1..n1\msupminus{}\}  \msubseteq{}r  \{m2...\}  supposing  m2  \mleq{}  m1

Date html generated: 2018_05_21-PM-00_03_57
Last ObjectModification: 2018_05_19-AM-07_10_32

Theory : int_1

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