Nuprl Lemma : rtermSubtract-left_wf

[v:rat_term()]. rtermSubtract-left(v) ∈ rat_term() supposing ↑rtermSubtract?(v)


Proof




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

Latex:
\mforall{}[v:rat\_term()].  rtermSubtract-left(v)  \mmember{}  rat\_term()  supposing  \muparrow{}rtermSubtract?(v)



Date html generated: 2019_10_29-AM-09_28_47
Last ObjectModification: 2019_03_31-PM-05_24_54

Theory : reals


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