### Nuprl Lemma : pand-right_wf

`∀[v:formula()]. pand-right(v) ∈ formula() supposing ↑pand?(v)`

Proof

Definitions occuring in Statement :  pand-right: `pand-right(v)` pand?: `pand?(v)` formula: `formula()` assert: `↑b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` ext-eq: `A ≡ B` and: `P ∧ Q` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` sq_type: `SQType(T)` guard: `{T}` eq_atom: `x =a y` ifthenelse: `if b then t else f fi ` pand?: `pand?(v)` pi1: `fst(t)` assert: `↑b` bfalse: `ff` false: `False` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` bnot: `¬bb` pand-right: `pand-right(v)` pi2: `snd(t)`
Lemmas referenced :  formula-ext eq_atom_wf bool_wf eqtt_to_assert assert_of_eq_atom subtype_base_sq atom_subtype_base eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_atom assert_wf pand?_wf formula_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction extract_by_obid promote_hyp sqequalHypSubstitution productElimination thin hypothesis_subsumption hypothesis hypothesisEquality applyEquality sqequalRule isectElimination tokenEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry independent_isectElimination instantiate cumulativity atomEquality dependent_functionElimination independent_functionElimination because_Cache voidElimination dependent_pairFormation

Latex:
\mforall{}[v:formula()].  pand-right(v)  \mmember{}  formula()  supposing  \muparrow{}pand?(v)

Date html generated: 2018_05_21-PM-08_50_33
Last ObjectModification: 2017_07_26-PM-06_13_36

Theory : general

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