Nuprl Lemma : radd_assoc
∀[a,b,c:ℝ]. (((a + b) + c) = (a + b + c))
Proof
Definitions occuring in Statement :
req: x = y,
radd: a + b,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
true: True,
squash: ↓T,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
radd-list-cons,
cons_wf,
real_wf,
nil_wf,
req_witness,
radd_wf,
radd-list_wf-bag,
list-subtype-bag,
subtype_rel_self,
equal_wf,
squash_wf,
true_wf,
radd_comm_eq,
iff_weakening_equal,
req_wf,
radd-as-radd-list,
req_functionality,
req_weakening,
req_inversion,
append_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
permutation_weakening,
permutation_functionality_wrt_permutation,
permutation-rotate-cons,
radd-list_functionality_wrt_permutation
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
applyEquality,
independent_isectElimination,
natural_numberEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
hyp_replacement,
applyLambdaEquality,
dependent_functionElimination,
voidElimination,
voidEquality
Latex:
\mforall{}[a,b,c:\mBbbR{}]. (((a + b) + c) = (a + b + c))
Date html generated:
2017_10_02-PM-07_15_32
Last ObjectModification:
2017_07_28-AM-07_20_32
Theory : reals
Home
Index