`∀[T:Type]. ∀[R:bag(T) ⟶ bag(T) ⟶ ℙ].`
`  (bag-admissable(T;as,bs.R[as;bs]) `` (∀as,bs:bag(T).  (sub-bag(T;as;bs) `` R[as;bs])))`

Proof

Definitions occuring in Statement :  bag-admissable: `bag-admissable(T;as,bs.R[as; bs])` sub-bag: `sub-bag(T;as;bs)` bag: `bag(T)` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` all: `∀x:A. B[x]` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` sub-bag: `sub-bag(T;as;bs)` exists: `∃x:A. B[x]` bag-admissable: `bag-admissable(T;as,bs.R[as; bs])` and: `P ∧ Q` member: `t ∈ T` prop: `ℙ` so_apply: `x[s1;s2]` so_lambda: `λ2x y.t[x; y]` guard: `{T}` top: `Top` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  equal_wf bag_wf sub-bag_wf bag-admissable_wf empty-bag_wf bag-empty-append squash_wf true_wf bag-append-comm bag-append_wf iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin cut hypothesis equalitySymmetry hyp_replacement applyLambdaEquality introduction extract_by_obid isectElimination cumulativity hypothesisEquality equalityTransitivity applyEquality functionExtensionality sqequalRule lambdaEquality functionEquality universeEquality dependent_functionElimination independent_functionElimination isect_memberEquality voidElimination voidEquality imageElimination because_Cache natural_numberEquality imageMemberEquality baseClosed independent_isectElimination

Latex:
\mforall{}[T:Type].  \mforall{}[R:bag(T)  {}\mrightarrow{}  bag(T)  {}\mrightarrow{}  \mBbbP{}].
(bag-admissable(T;as,bs.R[as;bs])  {}\mRightarrow{}  (\mforall{}as,bs:bag(T).    (sub-bag(T;as;bs)  {}\mRightarrow{}  R[as;bs])))

Date html generated: 2017_10_01-AM-09_05_09
Last ObjectModification: 2017_07_26-PM-04_45_06

Theory : bags

Home Index