Nuprl Lemma : radd-rminus-assoc
∀[x,y:ℝ]. (((x + -(x) + y) = y) ∧ ((-(x) + x + y) = y))
Proof
Definitions occuring in Statement :
req: x = y,
rminus: -(x),
radd: a + b,
real: ℝ,
uall: ∀[x:A]. B[x],
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
radd-rminus-both,
radd_functionality,
req_weakening,
radd-assoc,
req_functionality,
and_wf,
uall_wf,
radd-zero-both,
int-to-real_wf,
req_witness,
iff_weakening_equal,
rminus_wf,
radd_comm_eq,
radd_wf,
real_wf,
true_wf,
squash_wf,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairEquality,
isect_memberEquality,
addLevel,
uallFunctionality
Latex:
\mforall{}[x,y:\mBbbR{}]. (((x + -(x) + y) = y) \mwedge{} ((-(x) + x + y) = y))
Date html generated:
2016_05_18-AM-06_51_51
Last ObjectModification:
2016_01_17-AM-01_46_32
Theory : reals
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